Systems and methods for displaying a golf green and a predicted path of a putt on the golf green

ABSTRACT

A system for displaying information of a golf putt on a user device includes generating a digital terrain map of a golf green, determining a location of a cup, determining a location of a golf ball on the golf green in real time, calculating a projected path of a golf ball from the ball to the cup and displaying information of the ball location, cup location, projected path, aiming path and a flat surface equivalent distance on a user interface of the user device.

CROSS-REFERENCE TO RELATED APPLICATION

The present invention claims priority to U.S. Provisional PatentApplication Ser. No. 61/541,727 entitled SYSTEMS AND METHODS FORPREDICTING AND DISPLAYING AN OUTCOME OF AN EVENT filed on Sep. 30, 2011,the entirety of which is incorporated by this reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to systems and methods forquantifying and visualizing the likelihood of a physical event. Morespecifically, the present invention relates to systems and methods forquantifying and visualizing the difficulty or likelihood of alternativeoutcomes of a physical event such as a feat in sports. Still morespecifically, the present invention relates to systems and methods forcapturing, estimating and displaying the theoretical course that astruck golf ball will travel on a golf green from any pre-determinedpoint A toward any other pre-determined point B of alternative sizes.

2. Description of the Related Art

Mathematical models have been developed to simulate various events.Critics, sports fans, broadcasters, games-players and others debate andhave written about the difficulty or likelihood of an event. Yet, thereexists no systems or methods to accurately quantify the same for manyapplications. Furthermore, systems and methods to effectively provide auser with such information do not exist.

Systems and methods have been described in the art for providing agraphical representation of a path that a golf ball should travel toenter a cup on a putting green, where the projected path is superimposedon a live broadcast of a golf green from the resting position of a golfball to the cup. Such a system provides a colored path or line from thegolf ball to the hole while the camera is still. Any movement of thecamera would necessarily cause the superimposed path to appear offtarget. In addition, the golfer cannot interact with the superimposedputting path or gain any information from it.

One attempt in the art to overcome the shortcomings of prior art methodsand systems is disclosed in U.S. patent application Ser. No. 12/775,944to Sweeney, the entirety of which is incorporated by this reference.Sweeney discloses a method, apparatus and program for computing a path,starting velocity, aim angle and aim points for directing a putted golfball for a point on a golf course to another point and incorporatingsuch data into charts or electronic media. Sweeney also discloses ameans of determining the initial launch conditions and actual path aputted golf ball traveled given its starting and ending ball positions.Sweeney, however, fails to teach or suggest how the position of the balland cup are located, which is a critical aspect of providing a system inwhich the path of a putt from the ball to the cup can be accuratelypredicted. Moreover, Sweeney fails to teach or suggest any process forevaluating the difficulty of a particular putt or the locations on agreen where the difficulty of a putt may increase or decrease.

Thus, there exists in the art a need to provide a system and method forproviding real-time putting information to a golfer that is accurate,interactive, quickly accessible and easy to use. In addition, there is aneed in the art to provide a system and method for providing predictedresults of a putt from a putting location on a green to a cup in thegreen that utilizes accurate topographical data of the green to predictand display an optimal putting path on a graphical representation of thegreen where the graphical representation of the green may be a digitalimage of the green, a three dimensional image of the green or agraphical image of the green that provides contour information andpredicted zones for putts that are not optimally struck by the golfer.Presentation of such three dimensional images in oral form or providingaudible instruction would also be advantageous.

SUMMARY OF THE INVENTION

Accordingly, the present invention provides systems and methods forcalculating, predicting, disclosing and displaying the likelihood of anevent, such as a golf putt on a green. In a particular embodiment, asystem and method is provided for displaying a virtual golf putt eventor alternatively or in combination for announcing a textual, graphicaland/or audible narrative representation of the virtual golf putt eventcomprising determining the location of the ball, the location of thetarget (e.g., a golf hole or a selected area adjacent to or surroundinga golf hole) determining the terrain of the green and displaying orotherwise conveying (e.g., graphical, textual and/or audibly announcing)information of the ball location, target location and green terrain onor through a user interface.

In another embodiment, a system and method according to the presentinvention provides determining the difficulty of the putt and/ordetermining the parameters for a desired outcome of a putt.

In yet another embodiment, a system and method according to the presentinvention includes means for allowing a user to indicate on a device thelocation of the golf ball, utilizing a device or plurality of devicesthat capture and/or transmit actual or estimated hole positioninformation, photographing or otherwise capturing the relative locationof the stationary ball and utilizing image processing and/or utilizing adevice that transmits pre-determined position information and a devicethat determines orientation information.

In still another embodiment, a system and method according to thepresent invention includes displaying a representation of the terrain asa contour, color gradient, or vector field, determining the current holelocation and displaying information relative to the putt.

In yet another embodiment, a system and method according to the presentinvention includes displaying results from the most recent attempt atthe same hole, displaying results from a user selected past attempt orattempts at the same hole and/or displaying accumulated results from aplurality of past attempts at the same hole or plurality of holes.

In yet another embodiment, a system and method according to the presentinvention includes determining the difficulty of the putt by determiningthe solution space of a successful event defined as a single putt or aconcatenation of putts, determining the solution space of all eventsand/or comparing the solution space of a successful event to thesolution space of all events.

In still another embodiment, a system and method according to thepresent invention includes quantifying the solution spaces by ananalytic method and/or a numerical method.

In another embodiment, a system and method according to the presentinvention includes quantifying the solution spaces by modelingnon-linear dynamics associated with an event.

In yet another embodiment, a system and method according to the presentinvention includes modeling the non-linear dynamics by fitting sampledata to a piecewise linear curve, fitting sample data to a quadraticcurve, fitting sample data to a cubic spline, fitting sample data to ab-spline, fitting sample data to a linear combination of rationalfunctions and/or fitting sample data to a linear combination ofexponential functions.

In still another embodiment, a system and method according to thepresent invention includes modeling the terrain by utilizing accurate orapproximate measurement data.

In yet another embodiment, a system and method according to the presentinvention includes displaying information pertaining to the quantifiedlikelihood of accomplishing a successful single putt or successfulconcatenation of putts of a golf ball.

In another embodiment, a system and method according to the presentinvention includes providing a 3D simulation of an optimized linerepresenting the ideal outcome, computing a line representing a straightline between the object at it's initial position and the position at theideal outcome, rendering a target marker at a fixed or user defineddistance from the object at its initial position at the desired angle toachieve the ideal outcome, rendering an optimized line representing thepath of an optimized outcome, rendering the volume or surface area ofthe solution space of a successful event, rendering an animation of a 3Dmodel representing the ideal outcome, rendering an animation of a 3Dmodel representing the ideal outcome simultaneously with that of anactual outcome, comparing the path of an actual outcome to that of thesolution space, comparing the path of an actual outcome to that of theideal outcome and/or rendering parameters relative to achieving thesuccessful outcome.

In yet another embodiment, a system and method according to the presentinvention includes providing information that comprises a force orplurality of forces applied to achieve a successful event compared to aset of reasonable limits to provide information regarding relativeparameters (i.e., speed and direction) required to accomplish the eventsuccessfully.

In still another embodiment, a system and method according to thepresent invention includes providing information that comprises a flatsurface equivalent distance (FSED) or plurality of FSEDs applied toachieve a successful event compared to a set of reasonable limits toprovide information regarding relative velocity (which includes a speedcomponent and a direction component) required to accomplish the eventsuccessfully.

In yet another embodiment, a system and method according to the presentinvention includes determining the FSED limits by utilizing the greentopography for every hole location in a particular golf green, or subsetof a golf green.

In another embodiment, a system and method according to the presentinvention includes determining the location of the ball by receivingdata relevant to the ball, and the surroundings of the ball and/orcomputing the position of the ball relative to the surroundings.

In still another embodiment, a system and method according to thepresent invention includes determining the position of the ball byreceiving reflectance data of ball and the surroundings, receivingposition data of the location of the target, receiving position data ofthe location where the reflectance data were acquired, receivingorientation data at the event of acquiring the reflectance data,comparing reflectance data at received position and orientation toprecomputed model of reflectance data from said position and saidorientation, refining parameters of received position and orientation tobest match precomputed model, identifying the ball or plurality of ballsin reflectance data and computing position of the ball or plurality ofballs relative to the target.

In yet another embodiment, a system and method according to the presentinvention includes identifying the ball by selecting a desired ball froma plurality of identified balls.

In another embodiment, a system and method according to the presentinvention includes determining the position of the ball by receivingposition data of the location of the target, determining the distancefrom the ball to the target, determining the orientation angle from theball to the target, relative to a known orientation angle anddetermining the position of the ball from the received and determinedinformation.

In still another embodiment, a system and method according to thepresent invention includes determining the position of the ball byreceiving position data of the location of the ball, determining theorientation angle from the ball to the target, relative to a knownorientation angle and determining the position of the ball from thereceived and determined information.

In yet another embodiment, a system and method according to the presentinvention includes determining the position of the ball by receiving agraphical representation of the ball and said surroundings andidentifying the location of the ball relative to said surroundings.

In another embodiment, a system and method according to the presentinvention includes determining the position of the ball relative to thetarget by identifying the location of the target relative to saidsurroundings.

In another embodiment, a system and method according to the presentinvention includes determining the position of the ball relative to thetarget by receiving distance information relative to a plurality ofknown locations nearby the ball, receiving distance information of theball to said plurality of known locations, receiving distanceinformation of the target to said plurality of known locations anddetermining the position of the ball and target relative to thesurroundings.

In yet another embodiment, a system and method according to the presentinvention includes determining the position of the ball relative to thetarget by receiving position information of a location where a ball maybe placed relative to surroundings and receiving position information ofthe target relative to surroundings.

In still another embodiment, a system and method according to thepresent invention includes graphically illustrating a parameter used inquantifying the likelihood of a successful event on a smartphone, acomputer screen, a video game console, a television set, a hand heldelectronic device and/or a mechanism for providing visual information toa user.

In yet another embodiment, a system and method according to the presentinvention includes graphically illustrating the difficulty of asuccessful event as the inverse of the ratio of the size of thesuccessful solution space to the total solution space.

In yet another embodiment, a system and method according to the presentinvention includes pre-determining a grid of ideal outcomes and usingthe grid of pre-determined ideal parameters to determine the idealoutcome for any position of ball on the green and any correspondingposition of the target.

In another embodiment, a system and method according to the presentinvention includes determining the solution space for successful and allevents by establishing a first test putt, applying first test putt torelevant green topography, calculating a line of variance, calculatingsequential test putts and selecting an optimum sequential test putt.

In another embodiment, a system and method according to the presentinvention includes establishing a first test putt by establishing anorientation direction, establishing a cup position, establishing a firstball position and determine the first ball force stop position.Alternatively, a first test putt is established by establishing anorientation direction, establishing a cup position, establishing a firstball position and determine the ball speed at the location of the cup.

In yet another embodiment, a system and method according to the presentinvention includes selecting the optimum sequential test putt buyproducing a series of sequential test putts using the same ball force orspeed as applied on the first test putt only varying the angle,producing a series of sequential test putts using varied forces orspeeds for each of the sequential tests putts performed previously anddetermining a single putt that most closely resembles thecharacteristics of the ideal angle and force or speed or a plurality ofideal angles and forces or speeds.

In still another embodiment, a system and method according to thepresent invention includes determining parameters for a desired outcomeby determining an offset angle or plurality of offset angles associatedwith the ideal angle and force or speed and/or determining an offsetforce or speed or plurality of offset forces or speeds associated withthe ideal angle and force or speed or a plurality of ideal angles andforces or speeds.

In yet another embodiment, a system and method according to the presentinvention includes determining parameters for a desired outcome bydisplaying an amoeba-like territory indicating where the ball may stopif the putt force or speed applied is slightly greater than or slightlyless than the ideal force or speed and/or displaying an amoeba-liketerritory indicating where the ball may stop if the putt angle appliedis slightly clockwise or slightly counter-clockwise relative to theideal angle or plurality of ideal angles.

In still another embodiment, a system and method according to thepresent invention includes determining the ideal outcome by utilizingreal-world coordinates for the actual location of the ball, the cup, orother necessary parameters.

In another embodiment, a system and method according to the presentinvention includes determining the parameters for a desired outcome of aputt by determining the parameters for an optimal putt, determiningparameters for a 2-putt, at ball stop position, reverse engineer mostlikely path and/or at ball stop position, reverse engineer a pluralityof likely paths.

In yet another embodiment, a system and method according to the presentinvention includes allowing a user or plurality of users to utilizedisplayed information and recording data relative to utilizing displayedinformation.

In another embodiment, a system and method according to the presentinvention includes a control and variable experiment to determine thedegree of efficacy of the system and method of the present invention.

In still another embodiment, a system and method according to thepresent invention includes utilizing video media and adding orsubstituting narration.

In yet another embodiment, a system and method according to the presentinvention includes determining the position of the ball relative to thetarget by receiving distance information relative to a plurality ofknown locations nearby the ball, receiving distance information of theball to said plurality of known locations, receiving distanceinformation of the target to said plurality of known locations anddetermining the position of the ball and target relative to thesurroundings.

In another embodiment, a system and method according to the presentinvention includes determining the position of the ball relative to thetarget by receiving position information of a location where a ball maybe placed relative to surroundings and receiving position information ofthe target relative to surroundings.

In yet another embodiment, a system and method according to the presentinvention includes a method of acquiring utilization data by allowing auser or third party or plurality of users or third parties to recorddata by use with the system.

In still another embodiment, a system and method according to thepresent invention includes providing a control and variable experimentto determine the degree of efficacy of the system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a graphical display on a graphical interfacegraphically displaying a putting green and information relating to aputt of a golf ball on the golf green in accordance with the principlesof the present invention.

FIG. 2 illustrates a graphical display on a graphical interfacegraphically displaying a first menu for selecting a golf course of anapplication operated on a smartphone in accordance with the principlesof the present invention.

FIG. 3 illustrates a graphical display on a graphical interfacegraphically displaying a second menu for selecting a golf green of anapplication operated on a smartphone in accordance with the principlesof the present invention.

FIG. 4 illustrates a graphical display on a graphical interfacegraphically displaying a third menu for selecting display settings of anapplication operated on a smartphone in accordance with the principlesof the present invention.

FIG. 5 illustrates a graphical display on a graphical interfacegraphically displaying a fourth menu for selecting position settings ofan application operated on a smartphone in accordance with theprinciples of the present invention.

FIG. 6 illustrates a graphical display on a graphical interfacegraphically displaying a golf green displayed on a smartphone inaccordance with the principles of the present invention.

FIG. 7 illustrates a graphical display on a graphical interfacegraphically displaying a golf green displayed on a smartphone inaccordance with the principles of the present invention.

FIG. 7A is a graphical representation for determining the position of agolf ball on a green and a ball marker in accordance with the principlesof the present invention.

FIG. 7B illustrates the ball marker shown in FIG. 7A at variousorientations in accordance with the principles of the present invention.

FIG. 8 illustrates a graphical display on a graphical interfacegraphically displaying a golf green displayed on a smartphone inaccordance with the principles of the present invention.

FIG. 9 illustrates a graphical display on a graphical interfacegraphically displaying a golf green displayed on a smartphone inaccordance with the principles of the present invention.

FIG. 10 illustrates a graphical display on a graphical interfacegraphically displaying a golf green displayed on a smartphone inaccordance with the principles of the present invention.

FIG. 11 illustrates a graphical display on a graphical interfacegraphically displaying a golf green and putt information in accordancewith the principles of the present invention.

FIG. 12 illustrates a successful event and two alternative eventsrelative to a golf putt in accordance with the principles of the presentinvention.

FIG. 13 illustrates three successful events relative to a golf putt inaccordance with the principles of the present invention.

FIG. 14 illustrates three successful events relative to a golf putt inaccordance with the principles of the present invention.

FIG. 15 illustrates a surface area describing the successful solutionspace of a golf putt in accordance with the principles of the presentinvention.

FIG. 16 illustrates a graph describing the successful and entiresolution space of an event in accordance with the principles of thepresent invention.

FIG. 17 illustrates a presentation of information relative to achievinga hypothetical or actual event in accordance with the principles of thepresent invention.

FIG. 18 illustrates a graphical display on a graphical interfacegraphically displaying a putting green in accordance with the principlesof the present invention.

FIG. 19 illustrates a graphical display on a graphical interfacegraphically displaying a putting green in accordance with the principlesof the present invention.

FIG. 20 illustrates a graphical display on a graphical interfacegraphically displaying a putting green in accordance with the principlesof the present invention.

FIG. 21 illustrates a graphical display on a graphical interfacegraphically displaying a putting green in accordance with the principlesof the present invention.

FIG. 22 illustrates a graphical display on a graphical interfacegraphically displaying a putting green in accordance with the principlesof the present invention.

FIG. 23 illustrates a graphical display on a graphical interfacegraphically displaying a putting green in accordance with the principlesof the present invention.

FIG. 24 illustrates a graphical display on a graphical interface of adigital level and reference points for calibrating the user interfaceaccording to the principles of the present invention.

FIG. 25 illustrates a graphical display on a graphical interface of afirst measurement between a ball and a cup according to the principlesof the present invention.

FIG. 26 illustrates a graphical display on a graphical interface of asecond measurement between a ball and a cup according to the principlesof the present invention.

FIG. 27 is a side view of a user device for measuring a first distancebetween a ball and a cup according to the principles of the presentinvention.

FIG. 28 is a side view of a user device for measuring a second distancebetween a ball and a cup according to the principles of the presentinvention.

DETAILED DESCRIPTION OF ILLUSTRATED EMBODIMENTS

The present invention is directed to systems and methods of calculating,predicting and displaying various aspects of a putt to be made on aputting surface, including the computing, predicting and displaying thelikelihood of such an event. The likelihood of successfully making aputt may comprise determining the solution space of a successful putt,determining the solution space of all putts, and then comparing thesolution space of a successful putt to the solution space of all putts.One exemplary embodiment may include, without limitation, quantifyingnecessary input parameters to accomplish an ideal event, such as anideal angle and force applied in or speed of a golf putt, given a modelfor the terrain of the green and the location of a ball and of thegreen-cup.

Quantifying the solution spaces may utilize an analytic method or anumerical method. Either method, analytic or numerical, may be based inpart upon laws of physics such as Newton's Laws of motion, for example.There may also be non-linear dynamics that are difficult to quantifywith basic physics. Such instances may require quantifying the solutionspaces by mathematically modeling non-linear dynamics associated with anevent. Some methods for modeling the non-linear dynamics may include:fitting sample data to a piecewise linear curve; fitting sample data toa linear combination of rational functions; and/or fitting sample datato a linear combination of exponential functions.

Equations describing the translational motion of a golf ball may begiven by:

ma _(y) =f

Where m is the ball's mass, a_(y) is the translational acceleration andf is the force applied. The equation of rotational motion may be givenby:

Ia _(x) =nr−fR _(t)

Where I is the moment of inertia, a_(x) is the rotational acceleration,n is the normal force applied to the surface of the ball; r is theperpendicular distance of the point of contact from the center of mass;and Rt is the perpendicular distance between the tangential component ofthe contact force and the center of mass of the golf ball.

The contact force (direction and magnitude) for a ball rolling on anon-level surface can be computed by:

${\tan \mspace{11mu} \varphi} = \frac{{\rho_{g}\cos \; \theta \; \cos \; \phi \; \sin \; \beta} - {I_{b}\; \sin \; \theta}}{{\rho_{g}\; \cos \; \theta \; \cos \; \phi \; \cos \; \beta} - {I_{b}\; \cos \; \theta \; \sin \; \phi}}$and$f = {\frac{{\rho_{g}\cos \; \theta \; \cos \; \phi \; \sin \; \beta} - {I_{b}\sin \; \phi \; \cos \; \theta}}{\left( {1 + I_{b}} \right)\cos \; \varphi}{mg}}$

respectively. The acceleration in 2-dimensions (x and y) may then becomputed using:

ma _(x) =−mg sin θ−f sin φ,

and

ma _(y) =−mg cos θ sin φ−f cos φ,

respectively, so that the position at any point along the path may beeasily determined, predicted and/or displayed. Moreover thedetermination of a succession of such points will allow the predictionand/or display of the path of such object for initial resting point toultimate resting point.

Furthermore, modeling and execution of physical parameters may beimplemented by utilizing any one or combination of physics engines forpredicting motion of three-dimensional objects as they interact.

In one such embodiment, an image-recording device, such as a videocamera may be utilized to acquire motion data of a ball rolling across agreen. Image processing algorithms may be employed to automaticallytrack the motion of the ball, to identify the location of the center ofmass at specific instances in time. The motion may then be modeled, andthe resistive forces of the terrain may be quantified for variousinitial velocities or speeds. Furthermore, alternate methods may beemployed, including without limitation, rational functions orexponential functions. Another exemplary embodiment may include a highdefinition image-sensing device to detect the rotation of the ball andsimilar non-linear dynamics may be modeled thereby.

Another exemplary embodiment of the present invention may includecalculating a successful event wherein the successful event comprisesattaining an acceptable outcome and/or the ideal outcome. In a golfputt, for instance, the ideal outcome may be described as the balleventually stopping just inside and marginally below the topcircumference of the hole, where the center of mass of the ball isslightly over the edge of the hole, so that the ball falls into the holewith an acceptable velocity and trajectory. Such a condition wouldensure that if the angle of approach of the ball toward the hole werenot ideal, the ball would not roll far past the hole. Knowing that allputts that end up short of the hole have no possibility of being made,the end location of a short putt is also of interest and may becomputed, predicted and displayed using the current invention.

In this exemplary embodiment, the ideal force and angle for a putt on agreen based on a grid of ball locations on the green may be pre-computedto establish the ideal parameters for a putt, virtually anywhere on thegreen. A hand held device or pre-computed map will depict what line andwhat force to apply to any putt directed to any placed cup on anymodeled green. The green may be modeled by using modern LIDAR scanningdevices to produce a topographical map of the green at sub-centimeteraccuracy the captured data may have points that are several centimeters(e.g., 10 to 20 cm) apart with vertical accuracy several centimetersapart (e.g., approximately 3-5 centimeters). Using this an interpolatedDTM will be made and all computations will be made against theinterpolated DTM. Such digital rendition of a green by LIDAR scanningmay be referred to as a “digital terrain map or “DTM.” And other methodsof producing a DTM of a selected green are also incorporated into thecurrent invention. Of course, no perturbations must be assumed betweenthe date of scanning and the date of play, but largely that isacceptable, if the only “care” given to the green is watering, cuttingand sanding. The presence of ball marks, foot prints or other real lifeperturbations may or may not be accounted for in the calculations of thepresent invention.

One particular embodiment of a learning algorithm uses the followingabbreviations:

CP=Cup Placement

TN=True North or assumed True North

BP=Ball Placement

FTP=First Test Putt on the TN line

FBF=First Ball Force

FBF-SP=First Ball Force-Stop Position

FBL-SP=First Ball Line-Stop Position

RGT=Relevant Green Topography and is derived as the relevant part of theDTM of a given Green

LOV=Line of Variance from the assumed TN line and optimum FBF

STP=Sequential Test Putt (STPs are multiples of a STP)

STP-SP=Sequential Test Putt-Stop Position

STP-BF=Sequential Test Putt-Ball Force

VL=Variable Line

VF=Variable Force to “map” all putts to any cup placement position(“CP”) one must start somewhere.

One may start by orienting the green to a chosen “True North” (“TN”),which need not be accurate but may be approximate. In fact, except forvariations in friction due to orientation (such as direction of grassblade to or away from the sun) any orientation of the green isacceptable so long as one starts with a chosen TN line. The algorithmassumes a starting place for the first CP of an arbitrary distance, say100 cm, inside the most northerly point on the scanned green. Then onemay choose the same distance (100 cm) inside the fringe assuming thatgrounds keepers will place the cup, no nearer than that distance (100cm) from the fringe. But any other starting distance will be acceptable.Then, for the first CP, draw a line running due south from the first CP.This line is called the True North line (the “TN”). On the TN line, eachputt will come from a chosen Ball Placement (“BP”) in a filigree of BPsas if pearls on a string running from north to south all the way to thefringe. One may choose to start at 50 cm from the center of the first CPand this position is the first Ball Position (the first “BP”).

The ball will first be putted in the First Test Putt (the “FTP”) on theTN line, from the chosen BP and assuming that the green is flat and thatthe First Ball Force (the “FBF”) has been applied to the ball such thatthe FTP should stop at the First Ball Force Stop Position (the“FBF-SP”).

It is shown below that the FBF-SP is a function of the FBF only forhypothetical putts on the TN line if one assumes constant friction andflat topography for each FTP on the TN line:

${{{\frac{1}{2}I\; \omega^{2}} + {\frac{1}{2}{mv}^{2}} - {\int_{BP}^{{FBF} - {SP}}{{F_{friction} \cdot s}\ {s}}}} = 0},$

where F_(friction) is the force of friction of the green that slows downthe ball (always acting in opposition to the velocity of the ball, solong as the velocity is non-zero), s is the path that the ball travels(with the variable of integration, ds), I and m are the moment ofinertia and mass for a golf ball, respectively; w is the angularvelocity of a rolling golf ball; and v is the translational velocity ofthe ball.

The above equation can be reduced to:

${{\frac{1}{2}{v^{2}\left( {{4\pi^{2}R^{2}I} + m} \right)}} = {F_{friction}\left( {{FBF\_ SP} - {BP}} \right)}},$

when friction is considered to be constant. This, in turn, yields:

${{FBF\_ SP} = {{\frac{\frac{1}{2}{k\left( {{4\pi^{2}R^{2}I} + m} \right)}}{F_{friction}}{FBF}^{2}} + {BP}}},$

when solving for FBF-SP, and substituting k FBF² for v², due to theproportionality of velocity and force, from Newton's laws. Since allvalues in the equation above are known, except for FBF, the FBF-SP isclearly a function of only FBF.

Furthermore, the golf putt trajectory may be determined by utilizinganalytic geometry and physics. First, a two-dimensional surface within athree-dimensional space can be characterized by

z=σ(x,y).

One may assume that this is a single-valued function, that is, for every(x,y) point there is only one value of z, which is, of course,applicable for a golf green. One may define the function

G(x,y,z)=z−σ(x,y)

Whose value is G=0 on the surface.

Two important results from analytic geometry are the computation of thetangent plane and the normal vector to the tangent plane at an arbitrarypoint Po(xo,yo,s(xo,yo)) on the surface. These are

z=σ(x _(o) ,y _(o))+σ_(x)(x _(o) ,y _(o))(x−x _(o))+σ_(y)(x _(o) ,y_(o))(y−y _(o)) (tangent plane)

{right arrow over (n)}=∇G=−σ _(x)(x _(o) ,y _(o)){circumflex over (x)}−σ_(y)(x _(o) ,y _(o))ŷ+{circumflex over (z)} (normal vector)

Where s_(x) and s_(y) in the equations are defined to be

$\left. {{\sigma_{x}\left( {x_{o},y_{o}} \right)} \equiv \frac{\partial\sigma}{\partial x}} \middle| {}_{({x_{o},y_{o}})}{and} \right.$$\left. {{\sigma_{y}\left( {x_{o},y_{o}} \right)} \equiv \frac{\partial\sigma}{\partial y}} \middle| {}_{({x_{o},y_{o}})}. \right.$

The unit normal vector is

$\overset{\rightharpoonup}{n} = {\frac{{\sigma_{x}\hat{x}} - {\sigma_{y}\hat{y}} + \hat{z}}{\sqrt{1 + \sigma_{x}^{2} + \sigma_{y}^{2}}}\mspace{14mu} {evaluated}\mspace{14mu} {at}\mspace{14mu} {\left( {x_{o},y_{o}} \right).}}$

Take the direction of the normal vector to be in the positive zdirection for a flat, level plane (s(x,y)=const). The normal line thatgoes through the point Po and extends indefinitely in the sameorientation as the normal vector and be parameterized by t:

x=x _(o)−σ_(x)(x _(o) ,y _(o))t

y=y _(o)−σ_(y)(x _(o) ,y _(o))t

z=σ(x _(o) ,y _(o))−t

The rolling motion of the ball may be accounted for as follows. Arolling sphere spinning about its center point will have a moment ofinertia of

I=ξmr ²

where m is the mass of the sphere, r is its radius and the dimensionlesscoefficient x depends on the precise internal density profile of thesphere (x=2/5 if uniform).

The sphere is rolling along without slipping and no frictional losseswith linear translation velocity v. On a flat, level surface and gravityis not acting on the sphere, the motion will be uniform with noacceleration. Thus, no torque will be applied that will cause the ballto speed up or slow down. However, when the sphere experiences a changein incline, it will feel a component of gravity along its motion tocause it to accelerate. The linear acceleration a is related to theangular acceleration a=a/r by necessity and the assumption of noslipping during the sphere's rolling.

In motion along one direction, the equations for rolling withoutslipping and no friction are

ma = F_(g) − F_(torque) ${I\frac{a}{r}} = {F_{torque}r}$

where Fg is the component of gravity along the motion direction, andFtorque is the force applied to create a torque to generate the angularacceleration. Fg=mg sin q, where g=9.80 m/s2 is the acceleration due togravity, and q is the angle with which the normal vector to the surfacehas with respect to the z direction. These are two equations and twounknowns a and F_(torque). The solution is

${\left( {m + \frac{I}{r^{2}}} \right)a} = {m\; g\mspace{11mu} \sin \mspace{11mu} {\theta.}}$

Thus the motion is exactly the same as if it were a point particleexcept the additional inertia due to the energy of rolling is equivalentto adding an extra mass to the particle of size I/r². Including frictionto the rolling equation above yields

${\left( {m + \frac{I}{r^{2}}} \right)a} = {{m\; g\mspace{11mu} \sin \mspace{11mu} \theta} - F_{friction}}$

Generalized equations to the two-dimensional motion on a s surface:

(1+ξ)m{right arrow over (a)}=mg{right arrow over (Q)}−{right arrow over(F)} _(friction)

Since I=zmr2, the rolling of the sphere compared to a point particle ismodeled here as an effective increase of mass m:

m→(1+ξ)m

where x=2/5 if the sphere is of uniform density. The vector Q may bedefined to be:

$\overset{\rightarrow}{Q} = {\frac{\sigma_{x}\hat{x}}{\sqrt{1 + \sigma_{x}^{2} + \sigma_{y}^{2}}} - \frac{\sigma_{y}\hat{y}}{\sqrt{1 + \sigma_{x}^{2} + \sigma_{y}^{2}}}}$

For small angles s_(x), s_(y)<<1 then we can approximate Q as

{right arrow over (Q)}=−∇Vσ.

Friction may be modeled as the force that causes the slowing down of theball due to loss of energy (microscopically through heat dissipation),based on the normal force acting on the ball from the surface pushing uptimes a dimensionless coefficient of rolling friction C_(r).

${\overset{\rightarrow}{F}}_{friction} = {{C_{r}m\; {g\left( {\hat{n} \cdot \hat{z}} \right)}\hat{v}} = {\frac{c_{r}{mg}\hat{v}}{\sqrt{1 + \sigma_{x}^{2} + \sigma_{y}^{2}}} \cong {C_{r}m\; g\; \hat{v}}}}$

Where v is the direction of motion. Neglecting the additional effectivenormal force that the ball experiences by pushing against the green asit first begins to curve up hill or “lifting” off the green as it firstbegins to curve down hill.

Simply ignoring the velocity dependence of frictional effects gives us aconstant coefficient of rolling friction. The frictional force can bemodeled as:

{right arrow over (F)} _(friction) =C _(r) mg{circumflex over (v)},where

0.05≦C_(r)≦0.15

where the lowest values of C_(r) are the fastest greens and the highestvalues are the slowest greens. Standard techniques known to thoseskilled in the art can be employed to solve the differential equationalong the putt path.

Assuming the ball is at an initial position the present invention iscapable of determining the final position r_(f) upon stopping (e.g., afew inches past the cup). To do so, the correct initial velocity must bechosen. A first choice may not be the correct answer in general, and sovarious iterations of the initial velocity will occur in order toconverge to the final answer. A useful first guess may be to assume thatthe green is perfectly flat and solve the equation analytically. Theputt direction would be a straight line to the final position r_(f).

Another option may be to assume the putt to be at a specified non-zerospeed v_(f) at the cup position r_(cup). If the green is curved thenspecifying the ball come to rest a foot beyond the cup, for example,means that the center of the cup position may not be in the ball's path.

A first guess on the ball's speed using this criteria may beaccomplished by:

K _(i) =K _(f) +E _(friction)

which implies

${{\frac{1}{2}{mv}_{i}^{2}} + {\frac{1}{2}I\; \omega_{i}^{2}}} = {{1\; {mv}_{f}^{2}} + {\frac{1}{2}I\; \omega_{f}^{2}} + {C_{r}{mgd}}}$

where

d=|{right arrow over (r)} _(cup) −{right arrow over (r)} _(i)|

is the distance to the cup. However, we know that w=v/r, and we knowthat I=xmr², so we can solve the above equation for v_(i) simply as

$v_{i} = \sqrt{v_{f}^{2} + \frac{2C_{r}{gd}}{1 + \xi}}$

This should be the initial velocity choice, with the initial directionbeing pointed straight at the hole. Iterations of changing v_(i) and thedirection would be required to converge on the solution when thespecific topography of s(x, y) is included.

It will also be shown that the FBF-SP is a function of the FBF and theRelevant Green Topography (the “RGT” or “DTM”) for all putts after theFTP. For example, a FBF may be chosen to cause the ball to stop at, say,20 cm past the center of the CP for the FTP and RGT may cause this FTPto miss the CP such that (due to the RGT of up-hill, for example) theFBF-SP is actually 10 cm in front of the CP and 10 cm to the right.

The result of this FTP will then be applied to the RGT and the Line OfVariance to the line of the FTP (the “LOV”) will be noted and thecorresponding FBF-SP will be noted. Now, similar putts to the FTP willbe performed, each called a Sequential Test Putt and collectively calledSequential Test Putts (the “STP” and the “STPs”). The STPs will berepeated an optimum number of times as STPs and each such will benumbered sequentially, or alternatively numbered with a code of varianceof direction and force from the FTP. The repeat STPs will be performedusing a sequence of variances of the two variables of Variable Line (the“VL”) and Variable Force (the “VF”) from the FTP and the variances ofthe line produced and the BS position produced by the adjustments in VLand the VF will be noted.

From these multiple STPs the program will chose an optimum STP or agroup of nearly optimum STPs using the selection criteria describedbelow.

Here follows an exemplary embodiment:

First: Produce the FTP and apply it to the RGT. Note the LOV and theFBF-SP and the corresponding FBL-SP. Note that there will be no VF or VLin this first FTP, because it starts with the FTP and the assumedFBF-SP.

Second: Produce a set of 6 STPs using the same FBF as in the FTP butvarying the line from the TN line by 1, 2 & 3 degrees to the right and1, 2 &3 degrees to the left of the TNL each of these will have a LOV anda VL but no VF because of the use of the same test force, the FBF, as inthe FTP and again note the LOV and the STP-SP.

Third: Produce a second set of 24 STPs using 2 incrementally andmarginally greater forces or speeds and using 2 incrementally andmarginally lesser forces or speeds than the FBF applied thus 24 times intotal, 4 times to each of the first set of 6 STPs and again note the LOVand the STP-SP for each of these STPs.

Fourth: Now, from the 30 STPs choose a single putt that most closelyresembles the characteristics of the Ideal Wide Line Putt (the “IWLP”).

Note the LOV and the STP-SP of the chosen IWLP. If this results in anIWLP, then move to the next sequential BP (say a new BP of about 5 cmfurther South if the original BP was within 3 centimeters of the centerof the CP and new BP of about 10 cm if the original BP was furtherdistant than the chosen 10 cm adjustment) and repeat. It will be seenthat a different movement variable can be selected. If review of the 30STPs does not result in an IWLP, then repeat the previous steps usingthe optimal near-IWLP as the replacement TN line as the FTP.

When an IWLP is shown, the chosen IWLP will then serve as the SubstituteFTP (the “SFTP”) and substitute TN line and the process is repeated at 5cm, 10 cm and so on to the South, placing the new BP on the original TNline but using the most recent LOV as the new substitute TN line foreach successive SFTP until all IWLP's on that TN line have beenproduced. This process will then be repeated for all radiating lines tothe East and to the West of the TN line for the particular CP. And theprocess is further repeated for each new CP on the TN line. It will beseen that as the CP moves south on the TN line, the radiating lines tothe East and West of the TN line will expand from upwards of 90 degreesto approaching 180 degrees in each direction as the possible putts tothat CP expand around the CP for putts of direction East and West and upto putts of South direction and all directions in between.

A new CP will then be chosen on a grid built a chosen distance to theEast and to the West of the TN line and repeated until all suchsubstitute TN lines have been utilized and all CP on all such substituteTN lines have been used and all FTP and STPs on all such CP on all suchsubstitute TN lines have been computed to get the IWLP for each suchcombination. Specifications for the IWLP must be set. These can includecharacteristics of probability of the ball falling in the hole withincertain parameters of location, direction and speed. Such that with aforce of 3 traveling on a path due East and exactly parallel to theNorth edge of the cup, the ball will not drop unless that path is insidesaid edge by 3 cm, whereas if the ball is traveling not due East, but iscurving in a southerly direction it will drop if it is inside the saidedge by only 2 centimeters, even up to a force of 4. And so on.

Also, the wide line of the IWLP may show the greater force applied tothe right side of the line and the lesser force applied to the left sideof the line and so on. And probabilities can be produced from theevaluation of the number and magnitude of variations in the FBF and theLOV that can approximate the IWLP without actually being an IWLP. Forexample a 30 foot putt on a relatively flat slope may have a greaternumber of variables that will still result in an IWLP than a 15 footdown hill with a curve to the left. This is so, because of the increasein influence of the RGT over the LOV and the FBF.

Since any practical grid of ideal values has a limited number of pointsfrom which the ideal parameters were calculated, an estimation techniquemay be employed to estimate in real time, fluctuations in idealsolutions for actual ball placement between grid points. Otherembodiments an optimum line can be retrieved from a data base containinga plurality of stored, predetermined lines from a plurality of points Ato a plurality of points B on the DTM for a specific green DTM. One ofthe predetermined lines can then be retrieved from the databasecorresponding that most closely approximates the actual position of theball (point A) and cup (point B) on the green. These calculations can beperformed using linear, quadratic, cubic, sinusoidal or otherinterpolation techniques. One particular embodiment may comprise thecalculation of bare-eccentric coordinates of the ball relative to thenearest control points on the DTM. Then one may compute a weightedaverage on the neighboring ideal parametric values for force and anglefor the actual ball location as in:

F=F ₁ a ₁ +F ₂ a ₂ +F ₃ a ₃

Q=Q ₁ a ₁ +Q ₂ a ₂ +Q ₃ a ₃

where F is the ideal force at the actual ball position, F₁, F₂, and F₃,are the pre-computed forces at the three closest control points on theDTM; a₁, a₂, and a₃ are the pre-computed weighting factors that may bedetermined by computing the bare-eccentric coordinates, or some othermethod; Q is the ideal angle at the actual ball position; and Q₁, Q₂, Q₃are the pre-computed ideal angles at the three closest control points onthe DTM. Although the pre-calculation of the ideal parameters for allthe grid points may require significant computational execution, one canclearly see that a simple hand-held device can easily calculate a veryaccurate estimate of the ideal force and angle for any actual ballposition by utilizing the pre-determined parameters. Alternatively, ofcourse, all of the pre-computed IWLP can be stored in a database,computational grid or matrix. Then, for any given cup placement and ballplacement, the map or device need not “compute the IWLP, but rather itneed only retrieve it from the stored cup placement and ballplacement—just as a chess player does not “compute” the path of a rook'smove, but rather refers to pre-computed available moves for each givensituation.

It will be seen that the program can compute the relative difficulty ofany putt over any other putt, thus allowing teachers to caution studentsaway from putting from selected BP to selected CPs, with less thanpredetermined force, allowing players to make similar choices, allowingbroadcasters to advice viewing audiences of such relative probabilitiesamong several players, and allowing bookies and odds makers to wager onthe probability of success of alternative putts. For example, during alive golf tournament, once a golf ball lands on a green, utilizing theDTM information and difficulty of the ensuing putt from the ball to thecup on that particular green, the odds of the likelihood that the puttwill be made, given for example the putting accuracy of the golfer thatwill be attempting the putt, the contour of the green between the balland the cup, the resulting amount of break of the putt, the speed of thegreen, the slope of the green between the ball and the cup, and othersimilar factors and conditions.

Incorporation of a training golf ball that will record and calculate andreport relative force would add to the program by allowing students topractice relative force putts on chosen IWLPs thereby honing FBFcapabilities.

In order to display the IWLP, several aspects are present in the systemfor a given set of conditions.

First, a digital representation or approximation of the topography ofthe green of choice is created. For example, the green is scanned usingmodern LIDAR scanning cameras. The LIDAR scanning cameras may be mountedon aircraft for aerial scanning of greens or tripod mounted for groundscanning of greens to collect laser scan data. An Airborne LIDAR systemis typically composed of three main components: a laser scanner unit, aglobal positioning system (GPS) receiver, and an inertial measurementunit (IMU). The GPS receiver is used to record the aircraft trajectoryand the IMU unit measures the attitude of the aircraft (roll, pitch, andyaw or heading). The position and orientation information obtained fromthe GPS and IMU are used to determine target location with high accuracyin three-dimensional spaces. The three dimensional LIDAR points aretransformed into global coordinate system (GCS) data. While GPS data isprimarily used for latitudinal and longitudinal location of a point, theGCS data is particularly applicable in a three-dimensional geocoordinate system. After processing, the GCS data is used to create adigital elevation model (DEM). In order to generate the DEM from the GCSdata, the LIDAR points are separated into ground (terrain) andnon-ground (non-terrain) points, and as a result all the points areclassified to a bare earth model which contains the GCS information. TheGCS information, which includes GPS information, allows the data for aparticular green to be easily linked to a particular golf course.

The data files are converted into color elevation map, contour files anda Geotiff file. The DEM are used to create the digital terrain maps(DTMs) of the simulated golf greens of the present invention. The rawLIDAR data can be several gigabytes of data. Once converted into theDEM, the Geo reference images are relatively small in storage size thatcan then be used on a user device that may be limited in its internalcomputing power and/or memory, such as a smartphone.

By using LIDAR scanning, the topography of the green is measured andapproximated using a significantly large number of data points from astationary or moving location where the LIDAR scanning camera islocated. When creating the DTM from LIDAR data, it is possible that thegreen could be scanned using fewer data points and, by usingextrapolation techniques, the DTM can be created at points between thoseactually measured. Likewise, other methods known in the art could beused to capture the topography of the green. From such “real world” dataa CAD model of the green will be created and the portion of the greenthat is relevant to a chosen LOV will be concentrated to allow focus onthe Relevant Green Topography.

Next, the program will calculate and display the FBF and LOV for eachSequential Test Putt—STP, leading to the display, estimate orcomputation of an IWLP for every variable of CP and BP.

Additionally, in one variation of the invention, a means for real timecapture of the actual CP and BP for each putt is provided, so that theforegoing capabilities can be made available to the specified user inreal-time. Real-time capturing of the CP and BP on a green may beprovided by using GPS technologies and/or radio frequency tags. Forexample, two portable tags (the size of a poker chip or smaller) may beused. One will be used to mark the player's ball as the BP in the testcase—placed when the player picks-up his/her ball for cleaning—and theother will be used to mark the location of the cup, the CP—placed in thebottom of the cup when the player removes the flag, on in a moresophisticated scheme, placed in the bottom of the cup or on the pin bythe grounds keeper when the cup was set that morning. Alternatively, thelocation of the cup could be calculated by using a laser light directedto the pole of the flag before the flag is removed from the cup.Assuming that the location of the CP is know thru one or more of theseor other means, each of the players would then use his/her companionplayer chip to mark his/her respective BP. In rapid order, theselocations would be transmitted to a receiver, ground, portable orairborne and the IWLP for the respective BP's would be broadcast to thehand held device used by each player, to the broadcaster's booth and/orto other audiences. Because all possible IWLP had been previouslycalculated, the program needs only to know the two locations, CP and BPand the IWLP would be displayed.

Alternatively, a touch screen could be used and the player would beasked to estimate by touch the location of the CP and BP and then theIWLP would be displayed.

Alternatively, a paper map could be produced with chosen colors tosuggest the relative LOV and FBF needed from any neighborhood to anyother neighborhood and difficulty could be depicted.

In an additional iteration of the invention, the system or method wouldbe applied to select the Sequential Test Putts-Stop Position of the ballfor various pre-selected failed putts. For example one such STP-SP mightbe near the golfer's original BP on a putt up-hill that lackedsufficient ball force or speed to reach the cup and thus regresseddownhill after coming to a stop. Then the area of the several failedSTPs could be noted and color-coded to suggest worst to best near-missoutcomes, thus warning a golfer away from a too weak putt or a toosevere line putt in favor of a less risky choice.

Alternatively, it will be seen that the invention will allow the golferto select a cup of larger size when selecting a “two-putt” strategy. Inthis iteration, the ameba of possible area chosen will optimize thegolfer's selected favorite second putt position within the ameba ofchoice.

It can be seen that a method of business is available to the partyhaving these capabilities. That method might include the components ofscanning the greens, computing all possible IWLPs, capturing the CP eachday for said green and capturing serially the BP of several players orof storing predetermined ball lines and velocity. The resulting IWLPwould then be broadcast to the appropriate site (booth, hand held, andso on) and the course, the player or both, as applicable, would pay thebusiness. The business would include the system of capturing the scannedgreens and automating the topographical maps to harmonize with thealgorithm for calculating all possible IWLPs in the manner describedabove.

An additional system or method of the invention is presented at an earlytime and date before the method of capture of actual ball placement isperfected. For example, if a user were interested in golfer impressionor marketplace feed-back, the invention can be deployed to set on a testgreen a number, such as 20 for illustration, of small ball markers,placed in a manner of relative stability and without disruption to anygolfer or path of any given putt. Then, manual computation of the IWLPcould be calculated for these few test putts. A golfer could be invitedto test his/her own read of the green with out viewing the IWLP and thecompare with using the IWLP. Alternatively, a course management could beinvited to calculate the average time needed by four golfers to line-uptheir several putts when not-using and alternatively when using theIWLPs for the test BPs. The results can be recorded and allocations ofcapital and marketing approaches can be established with the informationgained at this early stage in deployment of the invention into commerce.

A variation of this early testing application of the invention could behad when the user wanted to test the use of the IWLP from any place ofBP on a given test green. Here, instead of transmitting the exactlocation of the Ball to a GPS satellite, the user would arrange forinstallation (for a short period and only for the benefit of this testcase) of sub stations around the green, from which, by triangulation,the exact location of the BP could be computed real time with the IWLPthen computed manually without the need or expectation of completeautomation.

In one embodiment, the present invention is embodied in a golf-relatedsoftware application (APP) that can be accessed and operated via asmartphone, such as the smartphone 10 illustrated in FIG. 1. Thesmartphone 10 includes a touch screen 11 that allows a user to viewcalculated information regarding the distance and direction of a putthat is displayed on the touch screen 11 and to select and/or manipulatecertain features of the APP 12. As shown in FIG. 1, the position of agolf ball 14 and cup 15 on a golf green 16 is illustrated in twographical representations. In the first graphical representation, abird's eye view is presented in which a straight distance line 17, aball trajectory line 18, an aiming line 19 and an aiming point line 20are displayed relative to the golf ball 14 and cup 15. Accompanying thestraight distance line 17 is a distance measurement representing theactual distance between the ball 14 and the cup 15. Accompanying theaiming point line 20 is an aiming point distance and arrow whichprovides the location of the aiming point 21 at which the user shouldaim in order to make the putt assuming that the user putts the ball atan appropriate speed.

An important aspect of the invention is the “Plays Like” feature 22,which provides a distance at which the putt will play like depending onthe slope of the green between the ball 14 and the cup 15. In thisexample, as shown in the second graphical representation 23, the ball 14is above the cup 15 by 6 inches resulting in a downhill putt. This PlaysLike feature 22 displays a distance measurement that takes intoconsideration the distance between the ball 14 and the cup 15 and theslope of the green. The plays like feature 22 distance thus provides arecalculated distance based on whether the putt is uphill or downhill,where plays like distances for downhill putts will be less than theactual distance 17 and uphill putts will be greater than the actualdistance. The user can then adjust the force of their putter to add ordecrease the effective distance of the putt according to the plays likedistance displayed.

The plays like distance is also represented in the second graphicalrepresentation 23 in which a second cup 24 is illustrated at a distancefrom the cup 15. In this example, the second cup 24 may be displayed ina different color in a shaded form so as to be visually distinguishablefrom the cup 15. Furthermore, in the second graphical representation 23,a cross-sectional contour of the green 25 is shown that illustrates thesurface of the green 25. All of the information presented on the screen11 of the smartphone 10 provides the user with sufficient information toincrease the likelihood that a putt of an actual golf ball on an actualgreen in the same position as represented on the screen will be made.This information is provided to the user in real-time so that the usercan use the information in for an actual putt. The system is adaptableso that the cross-sectional line 25 can be calculated on line 23 or online 18 as is most suitable to the user or other audience.

As illustrated in FIG. 2, the APP 12 includes various menus and submenusdisplayed on the screen 11 that allow a user to first select aparticular golf course that is to be played. A number of courses 26-30may be provided and stored in memory of the smartphone 10 and selectablevia the touchscreen 11. Additional courses can be accessed by scrollingto reveal courses listed below Course 5. Once a particular course hasbeen selected, the data representing the contours of the greens for thatparticular golf course that are stored in memory on the smartphone 10are used to provide information to the user, such as aiming points,trajectory lines and other information as shown in FIG. 1. As shown inFIG. 3, once the course has been selected, the user can select aparticular green to be accessed, including for example, the practicegreen 31 as well as holes 1-18. Once a particular green has beenselected, the smartphone will display a view of the green as selected bythe user. In order to alter or customize the image of the green andinformation displayed, the user can access the display settings menuillustrated in FIG. 4. The display settings allow the user to toggle onand off the various feature and information sets provided by the APP 12.For example, by turning on the “Basic” setting 32, the display willprovide basic information in text form only, such as distance to hole,amount (in distance) of right or left break of the putt, and the amount(in height) of incline or decline in the putt, that the change inelevation of the putt. The “Trajectory” setting 33 will add a graphicalrepresentation of the position and direction of an aiming point relativeto the cup at which the user should aim given a particular ball positionand cup position on the green in order to have the correct line of theputt. The “Line” setting 34 will display the curved or straight path ofthe putt from the ball to the cup that will allow the ball to enter thecup. The “Heat/Grid” setting 35 will display a color gradient in variouslocations on the green, for example, from red to green, with shades ofyellow and orange in between, that indicate locations on the green whereputts will likely be more difficult. The Heat/Grid setting can be chosento display contours, difficulty or vector fields over the DTM of thegreen.

As such, the Heat/Grid setting 35 can display locations on the greenwhere a second putt is more likely to be makeable so that the user canerr on a side of a cup where, if necessary, a second putt will likely beeasier to make. The “Elevations” setting 36 provides a display of thegreen in cross-section from the ball to the cup so that the user can seethe elevational changes in green between the ball and the cup.

As illustrated in FIG. 5, the APP 12 provides various position settingsthat can be toggled on or off by the user. In some instances, only oneposition setting can be activated if that position setting wouldnecessarily override another position setting. In the GPS setting 37,the position of the cup and ball on the green are determined by GPS. Inusing the GPS setting, the user (as shown in FIG. 6) is provided with aplan view of the green 38. Buttons 39 and 40 are provided for the cupand ball respectively as well as a mark button 41. When the user stepson the actual live green, the user can walk to the location of theactual cup, press the cup button 39 so that the APP 12 knows that theuser is going to mark the location of the cup 39. Pressing the markbutton 41 causes the APP 12 to mark the location of the cup using GPSdata. The mark button 41 once pressed provides a countdown timer inwhich an arm will sweep in a circular motion within the mark button 41to indicate to the user that the APP 12 is measuring the location of thecup. If the APP detects that the GPS location is changing during themeasurement, the countdown timer will slow so as to provide a moreaccurate measurement. That is, if the APP 12 detects that the GPSposition is changing, either the user (i.e., the smartphone 10) ismoving or the GPS location is still being calibrated based on the databeing received from the GPS satellites. In either case, the locationwill not be determined until the GPS data has stabilized for apredetermined period of time (e.g., 10 seconds). Once the GPS locationof the cup has been marked, the user can then walk to the location ofthe ball and repeat the process for the ball. Once the APP 12 hasdetermined, via GPS calculations, the location of the cup and ball, theputt data selected by the user will be displayed. Of course, those ofskill in the art will appreciate that other geo locating systems may beemployed in addition to or in replacement of use of GPS to locate theposition of the ball and cup. In the case of a graphical representationof the green as shown in FIG. 6, the ball 14 and cup 15 will be shown attheir measured locations relative to the graphical representation of thegreen 38.

As illustrated in FIG. 7, the use of electronic markers to mark thelocation of the cup and ball is also contemplated according the toprinciples of the present invention. The marker or markers may use radiofrequency technology or laser distance measurement to determine adistance from the cup to the ball and the location of the ball relativeto the cup. In this embodiment, the location of each cup has beenpredetermined for that given day for a particular golf course. Uponreaching the golf course, the user downloads the pin locations to theirsmartphone 10 so that the pin locations are predetermined for the APP12. When a user walks onto a green, the user marks the ball with anelectronic ball. The ball marker may include a digital compass to allowthe ball marker to know the direction of true north. By knowing truenorth, the distance from the cup and the angle between true north andthe direction of the marker to the cup, the APP 12 can calculate therelative position of the ball to the cup. If the cup position ispredetermined, the ball location can be calculated and displayed.

As illustrated in FIG. 7A, a ball marker 50 includes on one side thereofan alignment arrow 51 to be pointed at the direction of the cup. Theball marker 50 further includes an electronic compass 53 that can detectthe direction of True North and a processor/transmitter 54 to determinethe angle between True North and the straight line between the ball andthe cup and transmit that angle information to a smartphone running anAPP according to the principles of the present invention. As illustratedin FIG. 7A, where the ball marker 50 is positioned adjacent the ball(X2, Y2) and the distance D1 to the cup and the location of the Cup at(X1, Y1) is known, the position of the ball at (X2, Y2) can becalculated. Moreover, if the position of the cup at (X1, Y1) on thegreen is known, the precise position of the ball at (X2, Y2) can becalculated as illustrated in FIG. 7B. As shown in FIG. 7B, the cupdirection arrow will vary depending on the direction of the ball to thecup at any angle between 0 degrees and 360 degrees. The all ballpositions (X2, Y2) relative to the cup (X1, Y1) can be calculated forany measured angle Am between True North and the Cup Direction accordingto the following equations.

If 270>Am>180,

A2=Am−180,

X2=−(sin A2/D1) and

Y2=(cos A2/D1).

If 180>Am>90,

A2=180−Am,

X2=(sin A2/D1) and

Y2=(cos A2/D1).

If 90>Am>0,

A2=Am,

X2=(sin A2/D1) and

Y2=−(cos A2/D1).

Using these equations, some sample calculations (set forth in Table I)illustrate that the location of the ball (X2, Y2) can be calculated forany measured angle Am when the distance D1 between the ball and the cupis known.

TABLE I Am A2 D1 X2 Y2 360 0 20 0 −20.0 340 20 20 −6.8 −18.8 270 90 20−20 0.0 250 70 20 −18.8 6.8 180 0 20 0.0 20.0 150 30 20 10.0 17.3 90 9020 20.0 0.0 30 30 20 10 −17.3 0 0 20 0 −20.0

As shown in FIG. 8, the ball marker may also or alternatively include anRF chip therein that may be accompanied by a RF chip in the cup. Whenthe marker is placed on the green, the location of the marker can betriangulated relative to the cup where a RF beacon is provided near thegreen or at a central location on the golf course. The RF beaconprovides a third reference point for triangulating the position of themarker on the green relative to the cup. This information is thentransmitted to the APP 12. The APP 12 then displays the location of theball on the green 38 since the location of the cup 15 is already knownand displayed. Again, since there is some time involved in making thedistance measurement and calculation, a countdown timer in the markerbutton 41 may be provided to let the user know when the calculationshave been completed.

As illustrated in FIG. 9, the user setting allows the user to simplydrag and drop the approximate location of the ball using a ball pin 14′and a cup pin 15′. This is particularly useful and can be relativelyaccurate when an accurate representation of the green 38 and an adjacentgeographical object, such as a sand bunker 38′ is presented to providethe user with proper green orientation relative to the location of thepin and the ball. Once the user has set the ball pin 14′ and the cup pin15′, pressing the mark button 41 will cause the pins 14′ and 15′ to beset in place and the APP 12 to calculate the various putt information ofthe present invention. Alternatively, in one configuration of theinvention, this ball placement information is superimposed on the heatmap or other graphical representation of the DTM and the user can thenmore accurately suppose the line of the putt and the force required tomake the putt.

As shown in FIG. 10, the photo setting, the user, upon approaching agreen, will take a photograph of the green, for example, from a markedphoto spot adjacent the green. The APP 12, knowing that the photo istaken from a particular location and detecting the location of the balland the cup from the photograph will then position the ball 14 and cup15 on the green at their actual locations. This is done using imagerecognition software that determines the presence and location of theball and presence and location of the cup. For example, once the photois taken, the image recognition software locates a circular objecthaving a particular relative size and color that would likely be a golfball. Similarly, the photo recognition software locates an elongatestraight object indicating the pin and locates the bottom of that objectto determine the location of the cup. Once those two points are known,the software can then determine the relative position of the cup and theball on the green and use that data for the APP in displaying the ball,cup and putt information to the user.

Regardless of the method employed to determine the ball and cup locationon the green, once determined, the APP 12 uses this data to calculateand display information to the user regarding the proper path for theputt. As shown in FIG. 11, the location of the ball 14 and cup 15 aredisplayed on a graphical or photographical representation of the green38. In addition, putt information, such as distance between the ball 14and cup 15, amount of break in the putt, position of an aiming point formaking the put, plays like information depending on the slop of thegreen between the ball 14 and the cup 15 and true putting path aredisplayed on or superimposed over the green 38. As will be discussed inadditional embodiments, the green 38 may also be displayed as a contourmap, heat grid or other graphical representation in combination with theputt information shown in FIG. 11.

In order to calculate the proper path of a putt that is most likely tobe successful, FIG. 12 illustrates an example of three golf putt paths110, 120 and 130. The ball at its initial position 140 travels along oneof the three paths 110, 120, 130. Paths 110 and 130 representunsuccessful events since the ball does not touch the circlerepresenting the cup 100. The path 120 represents a successful putt ifthe ball stops just past the edge of the cup 100 so that it falls withinthe cup 100. In this particular embodiment, the paths 110, 120 and 130indicate that the surface of the green is sloped from right to left,causing the path of a rolling golf ball 140 to curve from right to left.Each path 110, 120 and 130 begins at the ball 140 with the angle ofdeparture of each path relative to the ball being the same. The varianceof each path 110, 120 and 130 is a result of the ball having a differentinitial velocity with the path 110 representing a putt that has toolittle initial velocity and thus falls to the left of the 100, the path130 representing a putt that has too much initial velocity and thus endsabove the hole 100 and path 120 representing a putt that has the correctinitial velocity and thus ends within the boundaries of the cup 100. Itshould be noted that while specific reference is made herein to the cup100 as the end target for the ball, the present invention furthercontemplates that the target may be a space chose by the user orcalculated by the system of the present invention so as to allow forpredetermined favoritism for a two-putt strategy, especially when theuser is faced with a more difficult first putt and/or when the systempredicts that more than two-putts is likely.

FIG. 13 illustrates three successful putt events wherein it may bedescribed as keeping the angle of departure constant while varying theinitial speed of the ball or force applied. The ball at initial position240 approaches the hole 200 through paths 210, 220, and 230. Path 210may represent the minimum force required for success at a given angle,while path 230 may represent the maximum force or speed required forsuccess at that same angle. Path 220 may represent the optimum solutionat the illustrated angle of departure.

FIG. 14 also illustrates three successful putting events; yet in thisexemplary embodiment, the initial angle of departure is varied as wellas the initial speed or impact force. The ball at position 340approaches the hole 300 through paths 310, 320, and 330. Path 310 mayrepresent the minimum force required for success at a first given angle.The path 330 may represent the maximum force or speed allowed forsuccess at an angle that is greater than the angle of departure for path310. Path 320 may represent the optimum solution at an angle that isbetween the angles of departure for paths 310 and 330 and at an initialvelocity that is between the minimum and maximum velocities for paths310 and 320.

Referring again to FIG. 1, to facilitate successful completion of asporting event, such as a golf putt, a straight line 17 may be renderedbetween the object at its initial position and the position at the idealoutcome, such as the hole. The present invention may also render atarget marker 21 at a fixed or user defined distance from the object atits initial position at the desired angle to achieve the ideal outcome.Another exemplary embodiment of the present invention may render atarget 24 marked at a flat surface equivalent distance (FSED) (PlaysLike distance) along the optimal angle of initial velocity. The FSED isthe distance at which the ball would travel along a straight line, ifthe ideal initial velocity were applied to the ball on a perfectly flatgolf green. The FSED quantity or Plays Like distance may provide theuser useful (i.e., practical) information as to how hard he or she needsto hit the ball to complete a successful putt. The FSED may bedetermined by utilizing the present invention on a virtual model of asurface that is perfectly flat. The equations for the trajectory of theball may be identical and the topography of the green may be simplified.

FIG. 14 illustrates a possible solution space, represented by the area Abetween paths 410 and 430 for a given initial speed of a golf ballrolling on a green. The ball 440 approaches the hole 400 at any spacebetween paths 410 and 430. The lined region between 410 and 430represents a successful solution space, or the solution space for agiven initial speed that results in a successful event, such as making aputt.

FIG. 16 illustrates a graphical representation of an exemplary solutionspace. The two-dimensional graph 500 shows a successful solution space520 based on two parameters: p1 530 and p2 540. The ideal solution 590for 530 and 540 is represented as a dot 590 within the successfulsolution space 520.

FIG. 17 illustrates an exemplary embodiment of visually representinginformation relative to the solution space of a successful event. Inthis particular embodiment, an absolute minimum force (Fmin) 610 appearsat the left end and an absolute maximum force (Fmax) 650 appears at theright end of FIG. 6. It is to be assumed for this particular embodimentthat these limits are representative of lower and upper bounds typicalfor putting on a golf green, respectively. A relative minimum force (Fa)630 and a relative maximum force (Fb) 640 illustrate the lower and upperlimits to attain a successful putt, given other known pre-set or userchosen parameters such as the speed of a green (Stemp meter reading),time of day, time of year, grass orientation or other local conditionsand/or the location of the hole and the location of the ball on theterrain surrounding the hole. It should be noted that the system of thepresent invention may or may not account for any or all of such localconditions. A line 620 is also provided to connect the peaks of alllines representing each force to provide clarity to the viewer. A usermay then view the provided information to assist in determiningparameters such as angle or initial speed to better achieve a desiredoutcome, such as making a putt.

The information may be a flat surface equivalent distance, an initialspeed, or other quantity. Furthermore, the visual representation may bea line on a 2D plane, a bar graph, a pie chart, or any other form.

The FSED limits may be pre-calculated based on the green topography forevery hole in a particular course, or subset of a course. For example,the farthest distance on the green at a particular hole may be used asthe upper limit for the FSED. Or, the farthest distance on a particularset of holes, front 9, back 9, all 18 for an entire course, additionallymay be utilized as the upper FSED limit.

As illustrated in FIG. 18, a graphical representation, generallyindicated at 700, of a putting green 702 is represented as a twodimensional contour map of the green 702. Such a graphicalrepresentation of the putting green 702 may be displayed on a smartphone704 or other handheld device, such as a tablet PC or the like, whichcomprises a display screen 705 and internal electronic components whichmay include but are not limited to a processor, memory, a GPS chip, atransceiver, a two-way communication device, such as BLUETOOTHtechnologies, a speaker, a camera, such as the devices illustrated anddescribe in U.S. Pat. No. 7,479,949 to Jobs et al., the entirety ofwhich is incorporated by this reference. The contour map of the green702 is provided with contour lines 710-716, where each contour linerepresents a particular change in elevation in the surface of the green710, such as 2, 4, 6 or 12 inch changes in elevation of the surface ofthe green 702 similar to elevational changes represented intopographical maps.

As illustrated in FIG. 19, a graphical representation, generallyindicated at 800, of a putting green 802 is represented as a twodimensional gradient map of the green 802. Such a graphicalrepresentation of the putting green 802 may be displayed on a smartphone 804 or other handheld device, such as a tablet PC or the like. Thegradient map of the green 802 is provided with color coded areas 810-816representing areas of incline within the green 802, wherein each colorcoded area represents a particular inclination change in the elevationin the surface of the green 810, such as a change of 2, 4, 6 or 12inches over a particular distance, such as 6, 12, 24 or 36 inches. Thehole is represented by circle 818 with an arrow 820 indicating thegeneral direction of the slope of the green relative to the hole 818.

As illustrated in FIG. 20, a graphical representation, generallyindicated at 900, of a putting green 902 is represented as atwo-dimensional difficulty map of the green 902. Such a graphicalrepresentation of the putting green 902 may be displayed on a smartphone 904 or other handheld device, such as a tablet PC or the like. Thedifficulty map of the green 902 is provided with color-coded areas910-914 representing areas of difficulty of the putt based on variousfactors. The factors may include both variable factors, such as theinitial speed and direction of the putt involved as well as constantfactors, such as the speed of the green, the distance from the cup 915,graphically represented by pin or flag 915, and the slope of the greenbetween any actual, possible or assumed ball location and the cup 915,incline within the green 902, wherein each color coded area represents aparticular inclination change in the elevation in the surface of thegreen 810, such as a change of 2, 4, 6 or 12 inches over a particulardistance, such as 6, 12, 24 or 36 inches. The various areas ofdifficulty from the area 914 surrounding the hole 915 to the areas 910and 913 that may represent the most difficult putts for a ball residingwithin one of these areas for a pin placement within the area 914 may bebased upon a calculation in which a range of percentages of making aputt from within a particular area or zone can be predetermined. Forexample, the areas 910 and 913 may represent the area in which a puttfrom that area has a relatively high probability of being missed, whilearea 911 represents the area in which a putt has a moderate probabilityof being missed, area 912 represents the area in which a putt has amoderate probability of being made and area 914 has a high probabilityof being made. Having this information prior to hitting a golf shot to agreen can provide a golfer with invaluable information. In mostinstances, when a golfer is hitting a golf ball to a green the golferwould like to know the positions on the green where a putt has a betterchance of being made and the positions on the green where a putt has agreater chance of being missed. The golfer can then aim to attempt toland the ball in the preferred areas and avoid the less-preferred areas.It should be noted that it may often be the case that the a mostpreferred area may not necessarily be concentric around the hole 915 asgreens often slope around the hole and thus, for example, may result inthe preferred area extending more below the hole than above the hole.Likewise, the difficulty may be measured by, for example, the size ofthe target area, whether the target area comprises an around orproximate the cup or just the cup itself or the relative difficulty ofseveral ball locations relative to the cup location on the display.

In calculating the difficulty of a particular putt for displaying thedifficulty map as illustrated, several factors may be taken intoconsideration, some of which may be variable factors and some of whichmay be constant factors. For example, the predicted likelihood that aparticular putt from Point A, where the ball resides, to Point B, wherethe cup resides may depend on the distance D from Point A to Point B,the speed S (Stemp reading) of the green, the change in elevation A Ebetween Point A and Point B, whether the change in elevation is positiveor negative, the transverse slope (ΔS) of the surface of the greenbetween point A and Point B, the added difficultly −S if the putt is adownhill putt, the number of discrete elevation changes (NE) betweenPoint A and Point B, the number of discrete transverse slope changes(NS) of the surface of the green between Point A and Point B, theproficiency (P) of the particular golfer attempting the putt for puttsof similar distance, the percentage of made putts (% M) from locationssimilar to Point A, etc.

Accordingly, the odds O in percentage of success of a particular puttmay be calculated as:

O=((P+%M)/2)(1/D)(1/ΔE)(1/−S)(1/ΔS)(1/NE)(1/NS)

That is, the Odds O are equal to the proficiency P of the golfer plusthe percentage of putts actually made by other golfers from a similarlocation divided by 2 with each of D, ΔE, ΔS, −S, NE and NS beinginversely applied so as to decrease the odds O as each of the factorsthat affect the likelihood of a successfully made putt increases. Itshould be noted that each of the factors D, ΔE, ΔS, −S, NE and NS maynot be in absolute numbers but included as determined functions based onreal world measurements. For example, the difficulty of a putt for aputt between 2 feet and 20 feet may not be a linear function. Moreover,the effect on the odds for a change in elevation may be represented by arange of numbers from, for example, 1-5, where no change in elevation isrepresented by the number 1 so as to have no effect on the calculation,while a sever elevation change (e.g., greater than five feet) is given afactor of 5. Likewise the change in slope may also be represented by arange of numbers from 1-5 for example, with a sever slope given a factorof 5, while no transverse slope to the putt is given a factor of 1 so asto not affect the odds O. The number of elevation NE and/or slopechanges NE between Point A and Point B may also be represented by arange of numbers in which no changes are represented by the number 1 soas to not affect the odds, while 2 actual measured changes may berepresented by a number between 1 and 2 in that the effect on the odds Oby the NE or NS are never greater than 50%. It is noted that not all ofthe various factors may be included in determining the odds. Forexample, it may be desired and sufficient to only use such factors asthe golfers proficiency, if known, the distance and the transverseslope.

For generating the difficulty map, various points, such as in a grid ofPoints A separated by a small distance (e.g., 6 inches) are applied tothe DTM of the green. Based on at least the distance D and change intransverse slope ΔS (i.e., the amount of projected break of the putt)from Point A to Point B, the difficulty map is calculated, wherelocations of a higher odds O are presented in a first color (e.g.,green) and locations of lower odds O are presented in a second color(e.g., red). The difficulty map can then be provided to the user beforean approach shot to the green. This allows the user to see where to landthe ball in order to have higher odds of making the subsequent putt. Itis often known on golf courses that balls left at certain locationsrelative to the cup result in putts that are virtually impossible tomake. In some instances, the best location on the green is not directlyat the pin. Knowing where to land the ball on the green can, in somecircumstances, make the difference between a par and a double bogie. Assuch, the difficulty map of the present invention can be viewed by theuser prior to hitting a golf ball onto the green. Once the ball is onthe green, the plot of the projected path in order to make the putt canbe superimposed over the difficulty map, or provided in other graphicalways as described and shown herein.

As illustrated in FIG. 21, a graphical representation, generallyindicated at 1000, of a putting green 1002 is represented as atwo-dimensional difficulty map of the green 1002. Such a graphicalrepresentation of the putting green 1002 may be displayed on a smartphone 1004 or other handheld device, such as a tablet PC or the like.The difficulty map of the green 1002 is provided with color-coded areas1010 and 1011, with area 1011 representing an area of likely missesrelative to the hole 1013 based on the initial ball position 1015.Factors used to calculate and display the area of likely misses 1011 mayinclude both variable factors, such as the initial speed and directionof the putt involved to be made as well as constant factors, such as thespeed of the green, the distance from the hole 1015 and the slope of thegreen between the ball 1015 and the hole 1013. The area of likely misses1011 may be based on a percentage deviation from an ideal putt having aparticular direction and speed. By varying one or both factors by apredetermined percentage, e.g., 5% or 10%, the graphical representationof this area 1011 of dispersion can be calculated and displayed. Thisinformation can provide the golfer with information such as what factorscan have the most dramatic effect on a miss. For example, by allowingthe golfer to fix the speed to the preferred speed and display missesbased on a 10% variance in direction, the golfer can see the preferredside of the hole 1013 to miss the putt and end up closer to the hole atthe end of the putt. Likewise, the golfer could fix the direction tothat of the preferred direction and vary the speed by 10% to see whetherit is better to err by leaving the putt short or by putting the ballpast the hole 1013. The area 1012 may be shaded in a gradient manneracross the green 1002 from one color, such as green nearest the hole1013 to another color, such as yellow, at locations 1014 furthest fromthe hole 1013 where the difficulty of a putt from that area is mostdifficult. As such, both the area of likely misses can be representedaround the hole 1013 while the putt difficult of putts from any locationon the green can be simultaneously displayed. Accordingly, the targetmay comprises a target area, represented by the circle surrounding thecup or hole 1013, which may be concentric with the hole 1013 asillustrated or offset relative to the hole 1013 so that, for example,the user is left with an uphill and relatively straight putt for asecond putt if the first putt is missed. In other words the target maybe a target area for a user that is interested in determining a goodposition to leave the ball after a first putt in order to have a betterchance of making a second putt. It is often the case that a hole 1013 isplaced in a location where a missed putt to one side of the hole 1013results in an easier second putt than if the first putt is left on theother side of the hole 1013. For example, when the green is severelysloped, a second putt that is from a location below the hole 1013 isgenerally easier to make than a putt of equivalent distance that isabove the hole 1013. In such an instance, the area below the hole 1013would be indicated as the target area.

Likewise, the present invention may determine the difficulty attainingan optimal initial velocity of a golf ball to best achieve a two-puttevent. The two-putt event may be characterized by achieving a first puttending position of the ball to be within a desired distance from thetarget or hole. All estimations in determining the likelihood of anevent, the solution space, or any other parameter disclosed herein maybe applied to a two-putt event. In this instance, the target may beestimated to be a circle of a larger radius (a desired distance awayfrom the hole) or a segmented space or ameba-like space adjacent to thecup. Since the target for golf putts is already a circle, the radiusparameter for the target may be changed, and all equations appliedanalogously to the two-putt event calculation.

The present invention may determine the position of the ball relative toa target or hole by receiving data relevant to the ball, and thesurroundings of the ball, and computing the position of the ballrelative to the surroundings. There are many different ways to determinethe position of the ball. Some exemplary embodiments of the presentinvention may include photography and image processing, globalpositioning systems (GPS), ball marker devices, radio frequencyidentification tags, a digital compass, or other method.

While technology is rapidly advancing for scanning of golf greens andthe creation and display of associated “digital terrain maps” (“DTM”), asignificant impediment has arisen to full utilization. To date, no onehas offered a simple method to capture the location of the ball duringreal-time play as a player approaches or enters upon the green. Thepresent invention provides a simple method that captures the location ofthe ball and displays that location on the DTM (e.g., large and remoteor small and local) with both the DTM and ball location displayed on amedia device such as a smartphone. The present invention may beseamlessly integrated into any putting aid or visualization tool and ina manner that will not retard the pace of play. Additionally, thepresent invention can capture and depict the ball location of more thanone player. Users of the present invention may include golfers,instructors (class room or live), broadcasters, gaming houses and pinplacement workers.

In one embodiment, the location of the pin or cup on each DTM of ascanned green may be assured through other means and that is included inthe system or method by other methods. In another embodiment, a golferor other person may capture and insert into the DTM the location of thecup. The present invention utilizes the capabilities of current “phonecamera” technology to align selected camera capture points within theapplicable DTM. After the golfer's ball is on the green, the cameraoperator (golfer, broadcast media, caddie or other person) positions thecamera in such location as to capture on camera a 2-D image showing thegolf ball of interest and the cup. The system and method can be employedeither before the pin is removed or during the time that the pin remainsin the cup (as when an “on-green” player awaits a pitch shot from an“off-green” player. The scene is then captured with the camera. Thecamera also captures and integrates, using known art, the bearing of thecaptured scene; that is, the scene is labeled with its facing direction,such as in land conveyancing descriptions, “North, 30 degrees, sevenminutes and 18 seconds West” where such description is chosen as themidline of the captured image. It is not necessary that the ball or pinbe exactly on such mid line, just that each be visible in the scene.Also, other orientation methods could also be deployed.

The camera operator then taps on the scene depicted on the camera (ormoves a cursor or icon) showing the location of the ball shown in thecaptured visualization (or “picture”) of the green. In one iteration ofthe invention, the operator does the same to capture the location of thecup. Alternatively the course manger could have determined the locationof the cup and conveyed that data to the method or data set of themethod prior to the initiation of play. Using applications alreadyavailable in current cameras, the associated X and Y location of theball point (and alternatively also the cup point) is sent to theassociated program application. Note, this conveyance is not of the GPSlocation but rather is just of the X and Y location within the relativescene captured by the camera. It is this X and Y location informationthat is superimposed into the DTM.

In at least one embodiment of this invention, a third point on the greenor its parameter can be similarly designated to give the system a thirdreference point, or the system can be so configured as to designate thelocation of the camera as such designated point. For example, a smallpermanent marker could be placed adjacent each putting green todesignate the designated camera point for that green so that the systemwould automatically know the orientation of the ball and cup relative tothat point once the picture was taken. The location of each permanentmarker could be provided on the graphical representation of the green onthe user interface so that the user will know prior to approaching thegreen the location of the permanent marker. The permanent marker may beplaced at a location where the entire green can be photographed within asingle picture and where all portions of the green are visible. Visualalignment markers on the screen may be provided to allow the user toalign the captured image with a predetermined position of the green onthe display screen so that the user can properly position the greenwithin the display. For example, for a given green at a given golfcourse, a graphical representation of the outline of the green may besuperimposed on the screen as the picture is being taken. The user wouldthen simply align the outline of the green with the actual green in theimage to be taken. Once the green is photographed, the ball and cuplocation may be automatically determined by the software as by utilizingimage recognition software or by allowing identification of the ball andcup by the user as by utilizing movable icons on the display to bepositioned on the photo of the green at the locations of the ball andcup. By knowing relatively precisely the location of the ball and thecup relative to the green, the system of the present invention canquickly and accurately calculate or retrieve from stored priorcalculations and display the optimum putting path for making the putt.

Once gathered, the reference points are then conveyed into theapplication and converted to be imposed into the DTM that has beenpreviously captured and recorded. The applicable DTM may be provided byvarious means. Such means might include, by way of illustration and notlimitation, a sensing unit built into the camera, being previously codedto align with that DTM within the method that is closest to the camera.Or the camera operator could choose a green from depicted alternativesshown on the screen using technology outside the scope of thisinvention. A prior designation may also be used.

Confidence intervals can be utilized in the method using computationspreviously accomplished and stored in a library of possible locations Aand B on any given green, the media screen can be informed that thelevel of confidence of the computed putting path is within X percent,irrespective of whether the exact location has been captured within achosen variance. For example, the method may inform the user that thecomputed line is reliable up to 90% for a variance of ball placement upto 6 inches. Or for example, that the computed putting path is reliableup to only 50% for any putt to the right of the hole for up to 3 inches.

Determining the position of the ball with photography and imageprocessing may comprise receiving reflectance data of ball and thesurroundings; receiving position data of the location of the target;receiving position data of the location where the reflectance data wereacquired; receiving orientation data at the event of acquiring thereflectance data; comparing reflectance data at received position andorientation to a precomputed model of reflectance data from saidposition and said orientation; refining parameters of received positionand orientation to best match precomputed model; identifying the ball orplurality of balls in reflectance data; computing position of the ballor plurality of balls relative to the target.

The user may identify the ball by selecting a desired ball from theplurality of balls identified. The user may indicate graphically, selectfrom a numerical list, use a touch screen, or other method.

The position of the ball may be determined by utilizing GPS datasufficiently nearby the flag and utilizing a device that may be placedon the hole as a golfer places for a ball marker as he or she waits tocomplete the putt. The ball may be located by then receiving positiondata of the location of the target, determining the distance from theball to the target; determining the orientation angle from the ball tothe target, relative to a known orientation angle; and determining theposition of the ball from the received and determined information.

Determining the position of the ball may comprise a radio frequencyidentification (RFID) tag and a digital compass. First, the presentinvention receives position data of the location of the ball, thendetermines the orientation angle from the ball to the target, relativeto a known orientation angle. Third, the present invention may determinethe position of the ball from the received and determined information.Determining the position of the ball may comprise utilizing user input.A user may identify the location of the ball relative to saidsurroundings.

As illustrated in FIG. 22, once the position of the ball 1115 and hole1113 is determined or inputted relative to the green 1102, a graphicalrepresentation 1200 of the ball 115 and hole 113 can be displayed over agraphical representation 1100 of the green 1102 on a smartphone 1104.The graphical representation 1100 of the green 1102 may be atwo-dimensional representation of the green as previously described, anaerial photograph of the green, a three-dimensional model of the greenor other representation. Once the ball 1115 and hole 1113 aregraphically represented on the green 1102, the preferred path 1111 ofthe putt can be calculated and displayed on the green 1102. Otherfeatures can be toggled between the putting line representation 1114currently being displayed and, for example, the 2-putt calculation 1112.Other options, maps and stats may also be provided and selectable withvarious buttons 1116, 1117 and 1118, respectively, on the smartphone1104 or other similar device.

Determining the position of the ball relative to the target, such as thecup on the green, may comprise receiving distance information relativeto a plurality of known locations nearby the ball, receiving distanceinformation of the ball to the plurality of known locations. receivingdistance information of the target to the plurality of known locations,and determining the position of the ball and target relative to thesurroundings. To do so, a RFID tag may be embedded in a ball marker. Asecond RFID tag may be placed in the cup or in a marker placed near thecup. Signals from the RFID tags can provide distance information todetermine the location of each of the golf ball and cup and relativedistance apart.

The position of the ball may be determined relative to the target byreceiving position information of a location where a ball may be placedrelative to surroundings and receiving position information of thetarget relative to surroundings. This may be accomplished by GPS,differential GPS, total station, or other methods known to those skilledin the art. For example, the user could position himself near the ballto obtain a first GPS position and near the hole for a second GPSposition, each GPS position being associated with the relative positionon the putting green.

The present invention may also acquire utilization data such as marketor product research, data for product enhancement, product promotion orother marketing utilization, or for any other use. Data may be acquiredby recording data as a user utilizes the system and methods of thepresent invention. Control and variable experiments may also beperformed to determine the degree of efficacy of the present invention.For example, one user may perform a task relative to a golf putt withoutthe use of the system and methods of the present invention while anotheruser utilizes the systems and methods of the present invention. Theresults could then be compared to determine the efficacy of the systemand methods of the present invention. Data acquired may be recorded,such as voice or video recording, to utilize the present invention inmarketing training or other uses.

In an exemplary embodiment, the terrain may be modeled by utilizingaccurate measurement data from a 3D spatial data acquisition device suchas a LiDAR scanner.

The present invention may furthermore utilize likelihood informationwherein information pertaining to the quantified likelihood ofaccomplishing an event is visually presented to a viewer. This maycomprise a 3D simulation, for example. A non-exhaustive list ofinformation that may be visually presented may include: recording a3-dimensional line representing the ideal outcome; rendering a3-dimensional line representing the ideal outcome; rendering a linerepresenting the path of an actual outcome; rendering the volume orsurface area of the solution space of a successful event; rendering ananimation of a 3D model representing the ideal outcome; rendering ananimation of a 3D model representing the ideal outcome simultaneouslywith that of an actual outcome; comparing the path of an actual outcometo that of the solution space; comparing the path of an actual outcometo that of the ideal outcome; or rendering parameters relative toachieving the successful outcome. Such renderings may include renderingsof the terrain or other objects to properly orient a viewer.

For example, as illustrated in FIG. 23, the terrain of the green 1202may be modeled by utilizing representative measurement data from a 3Dspatial data acquisition device such as a LIDAR scanner. In the case ofcapturing data representative of the terrain of the green, when theLIDAR scanner is being used, the permanent marker previously discussedcould be placed at the location of the LiDAR scanning for each green.That way, the resulting terrain data can be easily matched and utilizedto calculate the break of a putt between the golf ball and the cup. Thegraphical representation 1200 of the green 1202 may include anoverlaying grid or mesh 1204 that illustrates contours on the green 1202based on varying spacing between grid lines. In addition, the green 1202may comprise a three dimensional surface model that can be manipulatedby the user as by rotating and tilting the image of the green 1202 toallow the user to view the green from different angles and viewpoints,including viewing from directly behind the ball 1206 or hole 1208.Rotational or tilting of the green may be controlled by variousgesturing on a touch screen display of the smartphone 1203 such astwo-finger rotation, two-finger splitting and combinations thereof. Thegraphical representation 1200 also displays a preferred putting pathline 1210 as well as an aim point 1212 for the putter. In addition, thegraphical representation 1200 may include written instructions 1214 thatinclude aiming direction and relative speed of the putt. The relativespeed of the put may be a number representing a number within a scale.For example, a speed of 5 may represent a speed of a putt on a flatsurface, whereas a speed of 7 may represent a speed of a putt that isdownhill. Likewise, the smartphone 1203 may provide an audio cue withthe same information. For example, the smartphone could provide audioinstructions to the golfer such as, “Aim eighteen inches to the right ofthe hole. Putt is slightly downhill.” Other audio cues may also be used.

Referring now to FIGS. 24-28, there is illustrated another embodimentfor determining relatively precisely the distance from the ball to thecup. The process utilizes the camera, accelerometer, digital compass andprocessor of the electronic handheld device, in this case a smartphone1300. As a first step, as shown in FIG. 24, the user is provided with ameans for determining the height that the phone is to be held in orderto get the most accurate distance measurements using the smartphone1300. To do so, two marks are placed at a precise distance apart (e.g.,3 feet, 5 feet, etc.) on the floor. A virtual bubble level 1302 isdisplayed on the smartphone 1300 while the camera application isactivated. The virtual bubble 1302 may also be calibrated by operating acalibration mode in which the smartphone is placed on a level surfaceand so that the virtual bubble 1303 will be centered in the cross hairs1304. The user, while maintaining the virtual bubble 1303 in the centerof the cross-hairs 1304, raises or lowers the phone relative to thefloor until Point A cross hairs 1306 are centered on Point A and Point Bcross hairs 1307 are centered on Point B. At this point, which may be atapproximately waist height, the user is instructed to remember and/orrecord the precise height of the smartphone 1300 so that in the field,the height of the phone for measuring a distance from a ball to the cupcan be repeated. It is also contemplated that a custom height H could becalibrated so that the user can place the phone 1300 at, for example,belt buckle height, and the distance between cross-hairs 1306 and 1307can be manually adjusted by the user as by dragging and dropping so asto be a precise distance apart (e.g., 3 feet apart when the phone 1300is level at height H.

As shown in FIGS. 25 and 27, once calibrated, the system knows theprecise distance between Point A and Point B when viewed through thesmartphone camera at the set height H and when viewed from any of aplurality of positions selected from the environment of points A and B.That is, in use, when the smartphone is held at height H correspondingto the calibrated height previously discussed and level to the horizon,the distance between the cross hairs 1306 and 1307 will indicate adistance of, for example, 3 feet or 5 feet, when the distance D1 betweenthe ball 1308 and cup 1310 is three feet or 5 feet respectively, inorder to properly align the cross hairs 1306 and 1307 at height H. Inthis configuration, the phone will be substantially level to thehorizon. In a refined configuration, the need for level presentation maybe avoided and the smart phone will compute the delta from level as tobe plus in one direction and negative in the opposite direction suchthat these differences are taken into account using trigonometrycomputations known to those of skill in the art.

As show in FIGS. 26 and 28, in order to accommodate and measuredifferent distances (e.g., greater than three feet) from the ball to thehole, the smartphone 1300 will be angled at an angle A1 chosen from aplurality of angles starting at a relative minimum angle to capture bothobjects and extending to a less acute angle within the needed tolerancesof the smart phone so as to be able to view both the ball 1308 and thecup 1310. Furthermore, in order to place the ball 1308 in the crosshairs 1306 and the cup in the cross hairs 1307, because of limitationsin the field of view FV of the camera, the user may need to step backfrom the ball 1308 in order to have both the ball 1308 and cup 1310 inview. The distance D2 between the smartphone 1300 and the ball as shownin FIG. 28 can be calculated. That is, because the smartphone is apredetermined height H and at a detectable angle A to the horizon usingthe accelerometer of the smartphone, the distance D2 can be calculatedas D2=sin A1. The angle A2 between cross hair lines 1306′ and 1307′ isalso known. As the angle A1 is increased in order to increase theviewable area between the ball 1308 and the hole 1310, the distance D1from the ball 1308 to the cup 1310 is calculated as D2=sin(A1+A2)−D2.

Once the distance D1 between the ball 1308 and the cup 1310 iscalculated, if the position (i.e., coordinates) of the cup 1310 areknown relative to the DTM of the green, the system can then utilize thedigital compass of the smartphone 1300 to calculate and determine theposition of the ball 1308 relative to the cup as previously describedherein. To do so, the user would return the phone to a substantiallyhorizontal orientation so that the digital compass can determine thedirection of True North N in order to triangulate the position of theball relative to the cup on the DTM. The system of the present inventioncan then utilize this information to graphically display the ball on agraphical representation of the DTM on the display of the smartphone andplot and display other information for the user regarding a putt fromthe ball to the cup as previously described herein.

As set forth herein, the present invention provides a system fordetermining ball and cup locations on a green and projecting, conveyingor otherwise displaying information relating to a putt from the ball tothe cup. According to the present invention, the system for displayinginformation on a user interface relating to a golf putt on a golf greencomprises generating a digital terrain map of a golf green, determininga first approximate location of a cup in the golf green and generatingcup coordinates relative to the digital terrain map, inputting cupcoordinates of the approximate location of the cup for placement of thecup at a representative location on the digital terrain map, storing thedigital terrain map and the cup coordinates in memory of a user device,determining a second approximate location of a golf ball on a golf greenin real time and generating ball coordinates relative to the digitalterrain map, calculating a projected path of a golf ball from the ballcoordinates to the cup coordinates in which the golf ball is most likelyto travel from the ball coordinates to the cup coordinates, theprojected path based on a contour of the green represented by thedigital terrain map, velocity of the golf ball when traveling from theball coordinates to the cup coordinates and angle between a firststraight line between the ball coordinates and the cup coordinates and asecond straight line between the ball coordinates and an aiming pointthat is at a distance from the cup coordinates that is calculated to bethe location where a putt to the aiming point will most likely result ina successful putt as a result of the effect of the contour of the green,and displaying information of the ball location, cup location, projectedpath, aiming path and a plays like distance on a user interface of theuser device.

The system further includes determining the difficulty of the putt basedon the location of the golf ball relative to the cup and the contour ofthe digital terrain map and displaying information regarding thedifficulty of the putt on the display of the user device. Theinformation regarding the difficulty of the putt on the display of theuser device may comprise a probability of success of the putt. Theinformation regarding the difficulty of the putt on the display of theuser device may comprises a color gradient comprising a first colorindicating an easier location on the green for a successful putt and asecond color indicated a harder location on the green for a successfulputt. The displayed information may also include results from the mostrecent attempt at the same hole, results from a user selected pastattempt at the same hole and/or accumulated results from a plurality ofpast attempts at the same hole or plurality of holes.

The method for determining the location of the ball may compriseproviding means for a user to indicate on a device a location of a golfball, utilizing a device or plurality of devices that transmitpre-determined position information, photographing the ball andsurroundings and utilizing image processing or utilizing a device thattransmits pre-determined position information and a device thatdetermines orientation information. Determining the location of the ballmay also comprise generating a photograph of the ball and the cup withthe user device, and determining a distance between the ball and the cupfrom the photograph. Determining the location of the ball may alsocomprise detecting an angle of incline of the user device relative to ahorizon and using the angle of incline to accurately determine thedistance from the ball to the cup in from the photograph.

The location of the ball may also be determined by receiving dataregarding the ball, and the surroundings of the ball and computing theposition of the ball relative to the surroundings. Likewise, theposition of the ball may be determined by receiving reflectance data ofball and the surroundings, receiving position data of the location ofthe cup, receiving position data of the location where the reflectancedata were acquired, receiving orientation data when acquiring thereflectance data and comparing the reflectance data at the receivedposition and orientation to a precomputed model of reflectance data froma position and orientation substantially equivalent to the receivedposition and orientation data, refining parameters of received positionand orientation to best match the precomputed model, identifying a ballin reflectance data and computing position of the ball relative to thecup. as

The location of the ball may also be determined by receiving positiondata of the location of the cup, determining the distance from the ballto the cup, determining the orientation angle from the ball to the cup,relative to a known orientation angle and determining the position ofthe ball from the received position data and determined distance andorientation angle. Likewise the position of the ball may be determinedby receiving position data of the location of the ball, determining theorientation angle from the ball to the target, relative to a knownorientation angle and determining the position of the ball from thereceived and determined information. The position of the ball may befurther determined by receiving a graphical representation of the balland the surroundings and allowing a user to identify the location of theball and the cup relative to the surroundings. Likewise, determining theposition of the ball relative to the cup may include receiving distanceinformation relative to a plurality of known locations nearby the ball,receiving distance information of the ball to the plurality of knownlocations, receiving distance information of the cup to the plurality ofknown locations and determining the position of the ball and cuprelative to the surroundings.

In various aspects of the invention, the system determines and displaysinformation regarding the difficulty of the putt by determining thesolution space of a successful event, determining the solution space ofall events and comparing the solution space of a successful event to thesolution space of all events. When determining the solution space,non-linear dynamics associated with an event may be modeled by fittingsample data to a piecewise linear curve, fitting sample data to aquadratic curve, fitting sample data to a cubic spline, fitting sampledata to a b-spline, fitting sample data to a linear combination ofrational functions and fitting sample data to a linear combination ofexponential functions.

Additional information provided to the user may include at least oneflat surface equivalent distance (FSED) to achieve a successful puttcompared to a set of reasonable limits to provide information regardingrelative strength required to accomplish the successful putt. The FSEDlimits are determined by utilizing the green topography for every holelocation in a particular golf green, or subset of a golf green.Additional information may include graphically illustrating a parameterused in quantifying the likelihood of a successful event, graphicallyillustrating a difficulty of a successful putt as the inverse of theratio of the size of the successful solution space to the total solutionspace, such as a grid of ideal outcomes used to determine the idealoutcome for any position of ball on the green.

To determine a solution space for successful and all events the systemmay include establishing a first test putt, apply first test putt torelevant green topography, calculating a line of variance, calculatingsequential test putts and selecting an optimum sequential test putt. Inaddition, establishing a first test putt may include establishing anorientation direction, establishing a cup position, establishing a firstball position and determining the first ball stop position based on atleast one of force or velocity.

Selecting the optimum sequential test putt may comprise producing aseries of sequential test putts using the same ball force or speed asapplied on the first test putt only varying the angle, producing aseries of sequential test putts using varied forces or speeds for eachof the sequential tests putts performed previously and determining asingle putt that most closely resembles the characteristics of the idealangle and force or speed.

To determine the parameters for a desired outcome the system of thepresent invention determines an offset angle or plurality of offsetangles associated with the ideal angle and force or speed and determinesan offset force or speed or plurality of offset forces or speedsassociated with the ideal angle and force or speed. Subsequently, anamoeba-like territory indicating where the ball may stop if the puttforce or speed applied is slightly greater than or slightly less thanthe ideal force or speed can be displayed and an amoeba-like territoryindicating where the ball may stop if the putt angle applied is slightlyclockwise or slightly counter-clockwise relative to the ideal angle.

To determining an ideal outcome, real-world coordinates for the actuallocation of the ball, the cup, or other necessary parameters may beused. Likewise, the system of the present invention may be configured todetermine the parameters for an optimal putt, determine parameters for a2-putt, at ball stop position, reverse engineer most likely path, and atball stop position, reverse engineer a plurality of likely paths.

It is contemplated that the information displayed by the system of thepresent invention may include displaying a virtual golf putt andallowing a user or plurality of users to utilize the displayedinformation and recording data relative to the utilization of displayedinformation. The plurality of users can then utilize the system fordetermining a golf ball location, a target location and terraininformation of a putting green and recording data as the plurality ofusers utilize the system.

According to the present invention a constant coefficient of rollingfriction may be used by computing a friction force with the formulafriction {right arrow over (F)}_(friction)=C_(r)mg{circumflex over (v)}where C_(r) is the coefficient of rolling friction (typically between0.05 and 0.15), m is the mass of the ball, g is the gravitationalconstant and v is the velocity of the ball.

It is further contemplated that a desired outcome may comprise utilizinga calculated first guess for initial velocity. Utilizing a calculatedfirst guess for initial velocity may include employing the formula

${v_{i} = \sqrt{v_{f}^{2} + \frac{2C_{r}{gd}}{1 + \xi}}},$

where v_(i) is the initial velocity, v_(f) is the final velocity, C_(r)is the coefficient of rolling friction (typically between 0.05 and0.15), g is the gravitational constant, d is the distance from the ballto the hole, and ξ is the factor used in calculating the moment ofinertia based on the properties of the ball.

In determining parameters for a desired outcome a moment of inertia forthe golf ball may be utilized, which is determined by at least one ofthe formulas:

I=ξmr ²

I=Σr ² Δm

I=∫r ² dm

I=Σρr ² ΔV

I=∫ρr ² dV

where ξ is a factor determined by experimentation, m is the mass of theball, r is the radius of the ball, ρ is the density function of the ball(mass per unit volume) and V is volume, and where Σ suggests a numericalsolution and ∫ suggests an analytic solution.

Furthermore, the present invention may utilize information bygraphically illustrating a parameter used in quantifying the likelihoodof a successful event. An example of such a parameter may include aforce or plurality of forces applied to achieve a successful event,compared to a set of reasonable limits to provide information regardingrelative strength required to accomplish said event successfully.

Alternately, presenting information may include graphically illustratingthe difficulty of a successful event as the inverse of the ratio of thesize of the successful solution space to the total solution space. Sucha quantity infers the difficulty of accomplishing an event. If such aquantity is very large, the likelihood of accomplishing said event isvery small. Contrarily, if the quantified difficulty is small, thelikelihood of accomplishing the event is relatively high.

Determining parameters for a desired outcome may comprise in anexemplary embodiment: determining an offset angle or plurality of offsetangles associated with the ideal angle and force or speed; determiningan offset force or speed or plurality of offset forces or speedsassociated with the ideal angle and force or speed; displaying anamoeba-like territory indicating where the ball may stop if the puttforce or speed applied is slightly greater than or slightly less thanthe ideal force or speed; or displaying an amoeba-like territoryindicating where the ball may stop if the putt angle applied is slightlyclockwise or slightly counter-clockwise relative to the ideal angle.Such parameters may assist a golfer in deciding whether he or she shouldover or under strike the ball to prevent a large deviation relative tothe ideal outcome and an actual outcome. If, for example, over-strikingthe ball would most likely occur in a large deviation between the idealand actual outcomes, a golfer may choose to under-strike the ball toavoid taking an extra hit if the ball does not fall into the hole.Likewise, the angle may cause large deviations if hit too far clockwise,relative to the ideal angle, yet small deviations if hit too farcounter-clockwise, based on the green terrain, green speed, or otherfactors.

Graphically illustrating the information may include displaying pixelson a computer screen, a video game, a television set, a hand heldelectronic device, or other mechanism for providing visual informationto a user. Thus, while specific examples and embodiments of the presentinvention employ the use of a smartphone upon which an APP may beoperated, the present invention is not so limited and may be employedusing various electronic devices, including, but not limited to tablets,personal computers, a smartphone, a computer screen, a video gameconsole, a television set, a hand held electronic device, anelectro-mechanism for providing visual and audible information to a userand the like.

The illustrated embodiments of this invention are not limited to anyparticular individual feature disclosed herein, but include combinationsof them distinguished from the prior art in their features, functions,and/or results achieved. Features of the invention have been broadlydescribed so that the detailed descriptions that follow may be betterunderstood, and so that the contributions of this invention to the artsmay be better appreciated. Those skilled in the art who have the benefitof this invention, its teachings, and suggestions will appreciate thatthe conceptions of this disclosure may be used as a creative basis fordesigning other methods and systems for carrying out and practicing thepresent invention.

While there have been described various embodiments of the presentinvention, those skilled in the art will recognize that other andfurther changes and modifications may be made thereto without departmentfrom the spirit of the invention, and it is intended to claim all suchchanges and modifications that fall within the true scope of theinvention. It is also understood that, as used herein and in theappended claims, the singular forms “a,” “an,” and “the” include pluralreference, unless the context clearly dictates otherwise.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meanings as commonly understood by one of ordinary skillin the art to which this invention belongs. While various methods andsystems of the present invention are described herein, any methods orsystems similar or equivalent to those described herein may be used inthe practice or testing of the present invention. All references citedherein are incorporated by reference in their entirety and for allpurposes. In addition, while the foregoing advantages of the presentinvention are manifested in the illustrated embodiments of theinvention, a variety of changes can be made to the configuration, designand construction of the invention to achieve those advantages includingcombinations of components of the various embodiments. Hence, referenceherein to specific details of the structure and function of the presentinvention is by way of example only and not by way of limitation.

What is claimed is:
 1. A system for displaying information on a userinterface relating to a golf putt on a golf green comprising: generatinga digital terrain map of a golf green; determining a first approximatelocation of a target area on the golf green and generating target areacoordinates relative to the digital terrain map; inputting cupcoordinates of the approximate location of the cup for placement of thecup at a representative location on the digital terrain map; storing thedigital terrain map, the first approximate location of the target areaand the cup coordinates in memory of a user device; determining a secondapproximate location of a golf ball on the golf green in real time andgenerating ball coordinates relative to the digital terrain map;calculating a projected path of a golf ball from the ball coordinates tothe cup coordinates in which the golf ball is most likely to travel fromthe ball coordinates to the cup coordinates, the projected path based ona contour of the green represented by the digital terrain map, velocityof the golf ball when traveling from the ball coordinates to the cupcoordinates and angle between a first straight line between the ballcoordinates and the cup coordinates and a second straight line betweenthe ball coordinates, an aiming point that is at a distance from the cupcoordinates that is calculated to be a location where a putt to theaiming point will most likely result in a successful putt as a result ofthe effect of the contour of the green; displaying information of theball location, cup location, projected path, aiming path, target areaand a flat surface equivalent distance (FSED) on a user interface of theuser device.
 2. The system of claim 1, further comprising determiningthe difficulty of the putt based on the location of the golf ballrelative to the cup and the contour of the digital terrain map anddisplaying information regarding the difficulty of the putt on thedisplay of the user device.
 3. The system of claim 2, wherein theinformation regarding the difficulty of the putt on the display of theuser device comprises a probability of success of the putt.
 4. Thesystem of claim 2, wherein the information regarding the difficulty ofthe putt on the display of the user device comprises a color gradientcomprising a first color indicating an easier location on the green fora successful putt and a second color indicated a more difficult locationon the green for a successful putt.
 5. The system of claim 1, whereindetermining the location of the ball comprises at least one of:providing means for a user to indicate on a device a location of a golfball; utilizing a device or plurality of devices that transmitpre-determined position information; photographing the ball andsurroundings and utilizing image processing; and utilizing a device thattransmits pre-determined position information and a device thatdetermines orientation information.
 6. The system of claim 5, whereindetermining the location of the ball comprises generating a photographof the ball and the cup with the user device, and determining a distancebetween the ball and the cup from the photograph.
 7. The system of claim6, wherein determining the location of the ball comprises detecting anangle of incline of the user device relative to a horizon and using theangle of incline to accurately determine the distance from the ball tothe cup in from the photograph.
 8. The system of claim 1, whereindisplaying information further comprises at least one of: displayingresults from the most recent attempt at the same hole; displayingresults from a user selected past attempt at the same hole; anddisplaying accumulated results from a plurality of past attempts at thesame hole or plurality of holes.
 9. The system of claim 2, whereindetermining the difficulty of the putt comprises: determining a firstsolution space of a successful event; determining a second solutionspace of all events; and comparing the first solution space of asuccessful event to the solution second space of all events.
 10. Thesystem of claim 6, wherein determining the first and second solutionspaces comprises modeling non-linear dynamics associated with an event.11. The system of claim 8, wherein modeling the non-linear dynamicscomprises at least one of: fitting sample data to a piecewise linearcurve; fitting sample data to a quadratic curve; fitting sample data toa cubic spline; fitting sample data to a b-spline; fitting sample datato a linear combination of rational functions; and fitting sample datato a linear combination of exponential functions.
 12. The system ofclaim 1 wherein the information comprises at least one flat surfaceequivalent distance (FSED) applied to achieve a successful putt comparedto a set of reasonable limits to provide information regarding relativestrength required to accomplish the successful putt.
 13. The system ofclaim 12, wherein the FSED limits are determined by utilizing the greentopography for every hole location in a particular golf green, or subsetof a golf green.
 14. The system of claim 1 wherein determining thelocation of the ball comprises: receiving data regarding the ball, andthe surroundings of the ball; and computing the position of the ballrelative to the surroundings.
 15. The system of claim 1, whereindetermining the position of the ball further comprises: receivingreflectance data of ball and the surroundings; receiving position dataof the location of the cup; receiving position data of the locationwhere the reflectance data were acquired; receiving orientation datawhen acquiring the reflectance data; comparing the reflectance data atthe received position and orientation to a precomputed model ofreflectance data from a position and orientation substantiallyequivalent to the received position and orientation data; refiningparameters of received position and orientation to best match theprecomputed model; identifying a ball in reflectance data; and computingposition of the ball relative to the cup.
 16. The system of claim 15wherein determining the position of the ball further comprises:receiving position data of the location of the cup, determining thedistance from the ball to the cup; determining the orientation anglefrom the ball to the cup, relative to a known orientation angle; anddetermining the position of the ball from the received position data anddetermined distance and orientation angle.
 17. The system of claim 16,wherein determining the position of the ball further comprises:receiving position data of the location of the ball; determining theorientation angle from the ball to the target, relative to a knownorientation angle; and determining the position of the ball from thereceived and determined information.
 18. The system of claim 17 whereindetermining the position of the ball further comprises: receiving agraphical representation of the ball and said surroundings; and allowinga user to identify the location of the ball relative to thesurroundings.
 19. The system of claim 18, wherein determining theposition of the ball relative to the cup further comprises allowing theuser to identify the location of the cup relative to the surroundings.20. The system of claim 1, wherein determining the position of the ballrelative to the cup comprises: receiving distance information relativeto a plurality of known locations nearby the ball; receiving distanceinformation of the ball to the plurality of known locations; receivingdistance information of the cup to the plurality of known locations; anddetermining the position of the ball and cup relative to thesurroundings.
 21. The system of claim 1, wherein displaying informationcomprises graphically illustrating a parameter used in quantifying thelikelihood of a successful event.
 22. The system of claim 1, furthercomprising pre-determining a grid of ideal outcomes and using a grid ofpre-determined ideal parameters to determine an ideal outcome for anyposition of ball on the green.
 23. The system of claim 2 whereindetermining parameters for a desired outcome further comprises at leastone of: determining an offset angle or plurality of offset anglesassociated with the ideal angle and force or speed; and determining anoffset force or speed or plurality of offset forces or speeds associatedwith the ideal angle and force or speed.
 24. The system of claim 23,wherein determining parameters for a desired outcome further comprisesat least one of: displaying an amoeba-like territory indicating wherethe ball may stop if the putt force or speed applied is slightly greaterthan or slightly less than the ideal force or speed; and displaying anamoeba-like territory indicating where the ball may stop if the puttangle applied is slightly clockwise or slightly counter-clockwiserelative to the ideal angle.
 25. The system of claim 6 whereindetermining the ideal outcome further comprises utilizing real-worldcoordinates for the actual location of the ball, the cup, or othernecessary parameters.
 26. The system of claim 2 wherein determining theparameters for a desired outcome of a putt comprises at least one of:determining the parameters for an optimal putt; determining parametersfor a 2-putt; at ball stop position, reverse engineer most likely path;and at ball stop position, reverse engineer a plurality of likely paths.27. The system of claim 1, further comprising acquiring utilization datacomprising a plurality of users utilizing a system for determining agolf ball location, a target location and terrain information of aputting green and recording data as the plurality of users utilize thesystem.
 28. The system of claim 1, wherein calculating a projected pathcomprises utilizing a constant coefficient of rolling friction bycomputing a friction force with the formula {right arrow over(F)}_(friction)=C_(r)mg{circumflex over (v)} where C_(r) is thecoefficient of rolling friction, m is the mass of the ball, g is thegravitational constant and v is the velocity of the ball.
 29. The systemof claim 2, wherein calculating a projected path comprises utilizing acalculated first guess for initial velocity according to the formula${v_{i} = \sqrt{v_{f}^{2} + \frac{2C_{r}{gd}}{1 + \xi}}},$ where v_(i)is an initial velocity, v_(f) is a final velocity, C_(r) is acoefficient of rolling friction, g is a gravitational constant, d is adistance from the ball to the hole, and ξ is a factor used incalculating the moment of inertia based on the properties of the ball.30. The system of claim 1, wherein calculating parameters for a desiredoutcome further comprises utilizing a moment of inertia for the golfball determined by at least one of the formulas:I=ξmr ²I=Σr ² ΔmI=∫r ² dmI=Σρr ² ΔVI=∫ρr ² dV where ξ is a factor determined by experimentation, m is amass of the ball, r is a radius of the ball, ρ is a density of the balland V is volume.